Recent questions and answers in Combinatory

+24 votes

4 answers

1

GATE2005-44
What is the minimum number of ordered pairs of non-negative 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 $b \equiv d \mod 5$ $4$ $6$ $16$ $24$

answered 19 hours ago in Combinatory by tusharp Junior (695 points) | 2.4k views

0 votes

1 answer

2

Engineering mathematics
$\text{How many 5 letter word can be formed}$ $\text{from 6 a's,6 b's,6 c's,5 d's,5e's,4f's,4g's,3h's,3i's ?}$

answered 2 days ago in Combinatory by shreejeetp (153 points) | 21 views

+11 votes

3 answers

3

GATE1999-1.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n-1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above

answered 2 days ago in Combinatory by Prince Sindhiya Active (1.1k points) | 1.3k views

+11 votes

5 answers

4

TIFR2016-A-15
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? $13$ $12$ $11$ $10$ $9$

answered 5 days ago in Combinatory by Manoja Rajalakshmi A Active (3k points) | 389 views

0 votes

3 answers

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 ago in Combinatory by srestha Veteran (88.7k points) | 77 views

0 votes

0 answers

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 by Balaji Jegan Active (1.2k points) | 26 views

0 votes

1 answer

7

Rosen (Combinatorics)
I am not getting this. Can someone please explain using example. Thank you

answered Jul 6 in Combinatory by kavya kamish upadhya (127 points) | 63 views

+1 vote

2 answers

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 in Combinatory by Prateek Raghuvanshi Active (4.6k points) | 135 views

+1 vote

1 answer

9

Rosen(Generating combination)
I am not getting this condition. Can someone please explain that condition with that example.

answered Jul 5 in Combinatory by Deepakk Poonia (Dee) Boss (16.7k points) | 42 views

0 votes

1 answer

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 (n-1) options as we want exactly two 1's. so how could just C(n,r) is used here?

answered Jul 5 in Combinatory by Shubham Shukla 6 Active (2.5k points) | 31 views

+2 votes

2 answers

11

Mathmatics problem
how many 4 digit numbers possible whose sum is equal to 12 ?

answered Jul 5 in Combinatory by arungate Active (1.1k points) | 161 views

0 votes

0 answers

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 (695 points) | 13 views

0 votes

0 answers

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 1’s and 0’s and the property that every prefix of w has at least as many as 0’s as 1’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 points) | 41 views

+26 votes

5 answers

14

GATE2017-2-47
If the ordinary generating function of a sequence $\big \{a_n\big \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

answered Jul 1 in Combinatory by Prateek Raghuvanshi Active (4.6k points) | 3.6k views

0 votes

0 answers

15

Rosen Discrete Maths book. Recurrence Relations. Example #3

asked Jun 29 in Combinatory by Abhisek Das Active (1.3k points) | 12 views

0 votes

1 answer

16

The minimum no of comparisons required to find minimum and maximum of 100 numbers is __

answered Jun 29 in Combinatory by Abhinavg (325 points) | 29 views

0 votes

4 answers

17

Combinatorics-Kenneth Rosen(Ex 6.6-11)
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 Boss (10.7k points) | 149 views

0 votes

1 answer

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 Boss (10.7k points) | 41 views

0 votes

2 answers

19

Combinatorics-Kenneth 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 views

+31 votes

9 answers

20

GATE2015-3-5
The number of $4$ digit numbers having their digits in non-decreasing 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 Boss (10.2k points) | 2.7k views

0 votes

1 answer

21

Combinatorics- kenneth Rosen(ex 6.4 47e)

answered Jun 26 in Combinatory by srestha Veteran (88.7k points) | 100 views

0 votes

1 answer

22

Combinatorics-Kenneth Rosen (Ex6.4-45)
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

0 votes

0 answers

23

Combinatorics - Kenneth Rosen(Ex 6.4 7c)

asked Jun 25 in Combinatory by Ayush Upadhyaya Boss (10.2k points) | 43 views

0 votes

2 answers

24

Combinatorics-Kenneth 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 Veteran (88.7k points) | 62 views

0 votes

1 answer

25

Combinatorics-Kenneth Rosen(Ex 5.3-41)
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 Boss (17.3k points) | 22 views

0 votes

0 answers

26

Combinatorics-Kenneth 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 Boss (10.2k points) | 54 views

0 votes

1 answer

27

Combinatorics-Kenneth 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 Boss (10.7k points) | 28 views

0 votes

0 answers

28

Combinatorics-Self 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 Boss (10.2k points) | 46 views

0 votes

1 answer

29

Combinatorics-Self 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 Junior (521 points) | 34 views

0 votes

3 answers

30

NET nov-17 paper-2 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 points) | 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 by vijju532 (273 points) | 37 views

+25 votes

9 answers

32

GATE2014-1-49
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 in Combinatory by Kumar Ashish Junior (557 points) | 1.8k views

+9 votes

3 answers

33

GATE2003-34
$m$ 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 in Combinatory by Kumar Ashish Junior (557 points) | 1.3k views

0 votes

0 answers

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]

asked Jun 5 in Combinatory by Warlock lord Active (3.4k points) | 32 views

0 votes

1 answer

35

Mind Boggling question

answered Jun 3 in Combinatory by Kunal Kadian (131 points) | 85 views

0 votes

1 answer

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 x-y is divisible by 10

answered May 30 in Combinatory by Kushagra Chatterjee Loyal (8.2k points) | 21 views

+4 votes

2 answers

37

GATE1990-3-iii
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 Veteran (352k points) | 268 views

0 votes

2 answers

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 by Kaurbaljit Junior (529 points) | 81 views

+1 vote

1 answer

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 Loyal (8.2k points) | 51 views

+1 vote

1 answer

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 by Kushagra Chatterjee Loyal (8.2k points) | 35 views

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