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Recent questions and answers in Combinatory
+24
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4
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1
GATE200544
What is the minimum number of ordered pairs of nonnegative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
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gate2005
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2
Engineering mathematics
$\text{How many 5 letter word can be formed}$ $\text{from 6 a's,6 b's,6 c's,5 d's,5e's,4f's,4g's,3h's,3i's ?}$
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Combinatory
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3
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3
GATE19991.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above
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Combinatory
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4
TIFR2016A15
In a tournament with $7$ teams, each team plays one match with every other team. For each match, the team earns two points if it wins, one point if it ties, and no points if it loses. At the end of all matches, the teams are ordered in the descending ... is the minimum total number of points a team must earn in order to be guaranteed a place in the next round? $13$ $12$ $11$ $10$ $9$
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Combinatory
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tifr2016
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5
Self Doubt
How to evaluate this quickly? $\large\sum^{20}_{r=0}(1)^r\binom{r+2}{r}\\OR\\\large\sum^{20}_{r=0}(1)^r(r+2)(r+1)$
answered
6 days
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Combinatory
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srestha
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77
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6
Combinatorics Question on Bit Strings
How many bit strings of length 8 contain either three consecutive 0's or four consecutive 1's ? MY APPROACH : Initially, for 3 consecutive 0's: 000_ _ _ _ _ =>2^5 = 32 WAYS 1000_ _ _ _ =>2^4 = 16 WAYS _1000_ _ _ =>2^4 = 16 WAYS _ _1000_ ... =>2*3! = 12 WAYS so, total ways = 112 + 48  12 = 148 ways But answer is given as 147 ways. Where am I wrong?
[closed]
asked
Jul 6
in
Combinatory
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Balaji Jegan
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1.2k
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26
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permutationsandcombinations
counting
discretemathematics
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7
Rosen (Combinatorics)
I am not getting this. Can someone please explain using example. Thank you
answered
Jul 6
in
Combinatory
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kavya kamish upadhya
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127
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+1
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2
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8
Kenneth Rosen Ex.10 counting
How many ways are there to put four different employees into three indistinguishable offices when each office can contain any number of employees?
answered
Jul 5
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Combinatory
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Prateek Raghuvanshi
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135
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kennethrosen
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1
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9
Rosen(Generating combination)
I am not getting this condition. Can someone please explain that condition with that example.
answered
Jul 5
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Combinatory
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Deepakk Poonia (Dee)
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42
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10
Rosen(PnC)
Suppose we consider n=4 and r=2 then bit string formed is like b1,b2,b3,b4 where Bi is bit. Now to ensure exactly two 1's in any of these 4 places we can do it byc(4,2). After this suppose string look like 1,b2,b3,1 now for remaining two bits, each has (n1) options as we want exactly two 1's. so how could just C(n,r) is used here?
answered
Jul 5
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Combinatory
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Shubham Shukla 6
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31
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+2
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2
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11
Mathmatics problem
how many 4 digit numbers possible whose sum is equal to 12 ?
answered
Jul 5
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Combinatory
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arungate
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161
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0
votes
0
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12
Rosen Pigeonhole principle
Not getting highlighted part how ceil N/K will be greater or equal to r?
[closed]
asked
Jul 4
in
Combinatory
by
tusharp
Junior
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695
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13
views
pigeonholeprinciple
0
votes
0
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13
Question regarding Catalan Number
I have a question regarding Catalan Number. The question is as follows, Find the number of binary strings w of length 2n with an equal number of 1â€™s and 0â€™s and the property that every prefix of w has at least as many as 0â€™s as 1â€™s. Now i know the answer for this question is 2nCn/(n+1). I wanted to know how this question relates to Catalan number?
asked
Jul 1
in
Combinatory
by
noxevolution
(
23
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41
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discretemathematics
permutationsandcombinations
+26
votes
5
answers
14
GATE2017247
If the ordinary generating function of a sequence $\big \{a_n\big \}_{n=0}^\infty$ is $\large \frac{1+z}{(1z)^3}$, then $a_3a_0$ is equal to ___________ .
answered
Jul 1
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Combinatory
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Prateek Raghuvanshi
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3.6k
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gate20172
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0
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15
Rosen Discrete Maths book. Recurrence Relations. Example #3
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Jun 29
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Combinatory
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Abhisek Das
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12
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0
votes
1
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16
The minimum no of comparisons required to find minimum and maximum of 100 numbers is __
answered
Jun 29
in
Combinatory
by
Abhinavg
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325
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29
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testseries
0
votes
4
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17
CombinatoricsKenneth Rosen(Ex 6.611)
In how many different ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee? I got the first point that we need to ... set with 4 elements. But how to deal with the second part that most difficult job is assigned to the best employee?
answered
Jun 28
in
Combinatory
by
Soumya29
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149
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discretemathematics
inclusionexclusion
kennethrosen
0
votes
1
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18
combinatorics
let say there are three elements in a set {1,2,3}.find total #of 4 digit no. which are neither non decreasing nor non increasing.
answered
Jun 28
in
Combinatory
by
Soumya29
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10.7k
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41
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permutationsandcombinations
0
votes
2
answers
19
CombinatoricsKenneth Rosen(Ex 6.5)
How many bit strings of length eight do not contain six consecutive 0's?
answered
Jun 28
in
Combinatory
by
Rishav Kumar Singh
(
173
points)

73
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discretemathematics
kennethrosen
inclusionexclusion
+31
votes
9
answers
20
GATE201535
The number of $4$ digit numbers having their digits in nondecreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
answered
Jun 27
in
Combinatory
by
Ayush Upadhyaya
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10.2k
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2.7k
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gate20153
permutationsandcombinations
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0
votes
1
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21
Combinatorics kenneth Rosen(ex 6.4 47e)
answered
Jun 26
in
Combinatory
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srestha
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88.7k
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100
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kennethrosen
generatingfunctions
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0
votes
1
answer
22
CombinatoricsKenneth Rosen (Ex6.445)
Find a closed form for the exponential generating function for the sequence $\{ a_n \}$ where $a_n=\frac{1}{n+1}$ and the exponential generating function for the sequence $\{a_n\}$ is the series $\sum_{n=0}^{\infty}\frac{a_n}{n!}x^n$
answered
Jun 26
in
Combinatory
by
Aman Juyal
(
269
points)

81
views
discretemathematics
generatingfunctions
kennethrosen
0
votes
0
answers
23
Combinatorics  Kenneth Rosen(Ex 6.4 7c)
asked
Jun 25
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Combinatory
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Ayush Upadhyaya
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10.2k
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43
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kennethrosen
generatingfunctions
discretemathematics
0
votes
2
answers
24
CombinatoricsKenneth Rosen(Ex 5.3 31)
The english alphabet contains 21 consonants and five vowels.How many strings of six lowercase letters of the English alphabet contain (b)Exactly two vowels (d)At least two vowels For (b) part I solved it like choose 2 vowels from 5 in $\binom{5}{2}$ ways ... }*6!))$ and both of my answers don't match with the key in Rosen. Please let me know where I am wrong.
answered
Jun 24
in
Combinatory
by
srestha
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88.7k
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62
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discretemathematics
kennethrosen
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0
votes
1
answer
25
CombinatoricsKenneth Rosen(Ex 5.341)
How many ways are there for a horse race with three horses to finish if ties are possible.(Two or three horses may tie).
answered
Jun 24
in
Combinatory
by
Anu007
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17.3k
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22
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discretemathematics
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0
votes
0
answers
26
CombinatoricsKenneth Rosen (Ex 5.2 12)
How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs ($a_{1}$,$b_1$) and ($a_2,b_2)$ such that $a_1$ mod 5=$a_2$ mod 5 and $b_1$ mod 5=$b_2$ mod 5? My answer comes to be 26. Please confirm.
asked
Jun 23
in
Combinatory
by
Ayush Upadhyaya
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10.2k
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54
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pigeonholeprinciple
discretemathematics
0
votes
1
answer
27
CombinatoricsKenneth Rosen(Ex5.1 23c)
How many strings of three decimal digits can be formed such that they have exactly two digits that are 4's. My approach as to select 2 positions for these 4's in $\binom{3}{2}$ ways and the last bit will have 10 choices.Now I can permute the string formed in $ ... total such strings should be $\binom{3}{2}$ * 10*$\frac{3!}{2!}$ = 90. But the answer is 27. How?
answered
Jun 23
in
Combinatory
by
Soumya29
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10.7k
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28
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kennethrosen
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0
votes
0
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28
CombinatoricsSelf doubt
How many outcomes are possible when 10 coins are tossed? $X_{h} + X_{t}$ =10 where $X_{h}$ denotes the number of heads and it is $\geq$0 and $X_{t}$ denotes the number of tails which is also $\geq$0. This comes out to be .$_{10}^{2 ... Shouldn't the answer to the above problem be $2^{10}$ considering each coin can have 2 outcomes either heads or tails? Which one is correct?
asked
Jun 22
in
Combinatory
by
Ayush Upadhyaya
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10.2k
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46
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discretemathematics
permutationsandcombinations
0
votes
1
answer
29
CombinatoricsSelf Doubt
In how many ways can we arrange 4 boys and 3 girls in a straight line such that no two girls are together. One approach came to my mind was arrange 4 boys first=4! ways. Now 5 gaps created.Choose 3 for girls and arrange girls=5C3*3! ... !(total ways without restriction) why am I getting a different answer from the former case where I take boys first and then arrange girls?
answered
Jun 22
in
Combinatory
by
Sumeet Singh
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521
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34
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discretemathematics
permutationsandcombinations
0
votes
3
answers
30
NET nov17 paper2 Q8
Let P and Q be two propositions , ~(P<>Q) is equivalent to : a)P<>~Q b)~P<>Q c)~P<>~Q d)Q>P
answered
Jun 19
in
Combinatory
by
Ammu9682
(
25
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336
views
0
votes
0
answers
31
self doubt
number of integers in the set {0,1,2,3......,10000}which contain digit 5 exactly once ???? i got the 9*9*9*9 is it right???
asked
Jun 19
in
Combinatory
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vijju532
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273
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37
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discretemathematics
+25
votes
9
answers
32
GATE2014149
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4$pennant. The set of all possible $1$pennants is ${(1)}$, the set of all possible $2$pennants is ${( ... ), (1,2)}$. Note that the pennant $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10$pennants is________
answered
Jun 17
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Combinatory
by
Kumar Ashish
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557
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1.8k
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gate20141
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+9
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3
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33
GATE200334
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ balls? \(\left( \begin{array}{c} m  k \\ n  1 \end{array} \ ...  k \end{array} \right)\) \(\left( \begin{array}{c} m  kn + n + k  2 \\ n  k \end{array} \right)\)
answered
Jun 9
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Combinatory
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Kumar Ashish
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557
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1.3k
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gate2003
permutationsandcombinations
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0
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0
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34
Random
There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness. My thoughts: Since there have asked for probability to pick a "pair", we must consider those ... 6C1)/ 24C2 + (6C1 * 6C1)/ 24C2 = 6/23 Which is the correct approach and why? Why am I getting different results?
[closed]
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Jun 5
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Warlock lord
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probability
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35
Mind Boggling question
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131
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85
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discretemathematics
permutationsandcombinations
factorial
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36
Ace booklet
The minimum number of non negative integers we have to choose randomly so that there will be atleast two integers x and y such that x+y or xy is divisible by 10
answered
May 30
in
Combinatory
by
Kushagra Chatterjee
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21
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+4
votes
2
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37
GATE19903iii
Choose the correct alternatives (More than one may be correct). The number of rooted binary trees with $n$ nodes is, Equal to the number of ways of multiplying $(n+1)$ matrices. Equal to the number of ways of arranging $n$ out of $2 n$ distinct elements. Equal to $\frac{1}{(n+1)}\binom{2n}{n}$. Equal to $n!$.
answered
May 26
in
Combinatory
by
Arjun
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352k
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268
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gate1990
normal
permutationsandcombinations
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2
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38
#Combinatorics
#COMB There are $4$ boys and $6$ prizes are to be distributed among them such that each has at least $1$ prize. How many ways that can be done? My solution: $\text{Case 1 : 3 1 1 1}$ $\text{Case 2 : 2 2 1 11}$ $\text{Case 1 : C(6, ... My doubt is in the second case, am I not considering the prizes to be indistinguishable? I am confused in this regard. Please help me clear this doubt.
answered
May 26
in
Combinatory
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Kaurbaljit
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81
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39
Pigeonhole Principle (3)
Let $a_1,a_2,a_3,....a_{100}$ and $b_1,b_2,b_3,....b_{100}$ be any two permutations of the integers from $1$ to $100$. $a_1b_1,a_2b_2,a_3b_3,....,a_{100}b_{100}$ Prove that among the $100$ products given above there are two products whose difference is divisible by $100$.
answered
May 26
in
Combinatory
by
Kushagra Chatterjee
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8.2k
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40
Pigeonhole Principle (2)
Suppose a graph $G$ has $6$ nodes. Prove that either $G$ or $G'$ must contain a triangle. ($G'$ is the complement of $G$.) Prove it using pigeonhole principle.
answered
May 25
in
Combinatory
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Kushagra Chatterjee
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