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Combinatorics:
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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
2 days
ago
in
Combinatory
by
vijju532
(
61
points)

23
views
discretemathematics
0
votes
0
answers
2
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)

31
views
probability
0
votes
1
answer
3
Mind Boggling question
asked
Jun 3
in
Combinatory
by
Balaji Jegan
Active
(
1.1k
points)

79
views
discretemathematics
permutationsandcombinations
factorial
0
votes
1
answer
4
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
asked
May 30
in
Combinatory
by
Rahul singh dhakrey
(
25
points)

20
views
0
votes
2
answers
5
#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.
asked
May 25
in
Combinatory
by
Abhisek Das
Active
(
1.3k
points)

77
views
permutationsandcombinations
discretemathematics
+1
vote
1
answer
6
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 $100$.
asked
May 25
in
Combinatory
by
Sammohan Ganguly
(
417
points)

48
views
pigeonholeprinciple
permutationsandcombinations
+1
vote
1
answer
7
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.
asked
May 25
in
Combinatory
by
Sammohan Ganguly
(
417
points)

27
views
pigeonholeprinciple
permutationsandcombinations
counting
+2
votes
1
answer
8
Pigeon hole (1)
Prove that out of hundred whole numbers one will always have $15$ of them such that the difference between any two of these $15$ numbers is divisible by $7$.
asked
May 25
in
Combinatory
by
Sammohan Ganguly
(
417
points)

30
views
pigeonholeprinciple
permutationsandcombinations
+1
vote
1
answer
9
Pigeon hole
Show that in a group of $n$ people there are two who have identical number of friends in that group.
asked
May 25
in
Combinatory
by
Sammohan Ganguly
(
417
points)

28
views
pigeonholeprinciple
permutationsandcombinations
0
votes
1
answer
10
Combinatorics
Find the number of seven digit integers with sum of the digits equal to $11$ and formed by using the digits $1,2$ and $3$ only. Soln $X_{1}+X_{2}+.......X_{7}=11$ $(x+x^{2}+x^{3})^{7}$ $(x(1+x+x^{2}))^{7}$ $x^{7}(1+x+x^{2})^{7}$ $x^{7}(\dfrac{1x^{3}}{1x})^ ... (x)3k) * ((7+k1k) xk) $((\binom{7}{k}) (x)^{3k}) \times (\binom{7+k1}{k} x^{k})$ Now not able to proceed. Kindly help.
asked
May 23
in
Combinatory
by
mbisht
(
161
points)

47
views
engineeringmathematics
generatingfunctions
discretemathematics
counting
0
votes
1
answer
11
query about partitionproblems in combinatorics
asked
May 22
in
Combinatory
by
mbisht
(
161
points)

33
views
0
votes
2
answers
12
ISIMTECHCSE2018
One needs to choose six real numbers $x_1,x_2,....,x_6$ such that the product of any five of them is equal to other number. The number of such choices is $3$ $33$ $63$ $93$
asked
May 20
in
Combinatory
by
jjayantamahata
Active
(
1.5k
points)

158
views
userisi2018
usermod
numbersystem
permutationsandcombinations
+1
vote
4
answers
13
kennneth rosen chapter counting
1. Find the coefficient of $x^{10}$ in the power series. $\left ( 1+x^{2}+x^{4}+x^{6}+x^{8}+.... \right )\left ( 1+x^{4}+x^{8}+x^{12}+.... \right )\left ( 1+x^{6}+x^{12}+x^{18}+.... \right )$ Ans. $\frac{1}{\left ( 1x^ ... \right )\left ( 1x^{6} \right )}$........now not able to proceed. 2.Provide a closed formula for the sequence it determines x2+3x+7+(1/(1x2))
asked
May 18
in
Combinatory
by
mbisht
(
161
points)

144
views
generatingfunctions
0
votes
2
answers
14
Generating Function
Find $\left [ x^{50} \right ]$ $\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
asked
May 18
in
Combinatory
by
Nils
Junior
(
881
points)

68
views
generatingfunctions
0
votes
1
answer
15
Generating function
1. Find a closed form for the generating function for the sequence $1,1,0,1,1,1,1,1,1,1,...........$ 2. Find a closed form for the generating function for the sequence $a_n= 2n+3$ for all $n=0,1,2,....$
asked
May 17
in
Combinatory
by
mbisht
(
161
points)

48
views
engineeringmathematics
generatingfunctions
0
votes
1
answer
16
kenneth rosen chapter 5 exercise 5.5 ques 51
asked
May 17
in
Combinatory
by
mbisht
(
161
points)

78
views
0
votes
0
answers
17
ISI 2018 MMA 1
The number of common terms in the two sequence (3,7,11,...,407} and {2,9,16,...,70} is A)13 B)14 C)15 D)16
[closed]
asked
May 14
in
Combinatory
by
Tesla!
Boss
(
16.1k
points)

51
views
userisi2018
usermod
sequenceseries
0
votes
2
answers
18
combinatorics
There were 4 blue french horns, 5 yellow Umbrellas and 6 Suits in a shop. Ted, Barney, Lily, Marshal and Robin came to the shop to buy the items. How many different results could have been recorded if all of the items were sold?
asked
May 5
in
Combinatory
by
gow tham
(
39
points)

70
views
permutationsandcombinations
engineeringmathematics
0
votes
2
answers
19
ISI 2014 PCB A2
Let m and n be two integers such that m ≥ n ≥ 1. Count the number of functions f : {1, 2, · · · , n} → {1, 2, · · · , m} of the following two types: (a) strictly increasing; i.e., whenever x < y, f(x) < f(y), and (b) nondecreasing; i.e., whenever x < y, f(x) ≤ f(y).
asked
May 1
in
Combinatory
by
tathatj
(
67
points)

84
views
isi2014
settheory&algebra
+3
votes
1
answer
20
Discrete Maths Kenneth Rosen chapter 6.3 Question 24
asked
Apr 30
in
Combinatory
by
surajumang08
(
189
points)

84
views
kennethrosen
counting
permutationsandcombinations
+1
vote
1
answer
21
ISI 2017 PCB A2
Let $a,b,c$ and $d$ be real number such that $a+b=c+d$ and $ab=cd$. Prove that $a^{n}+b^{n}=c^{n}+d^{n}$ for all positive integer $n$.
asked
Apr 28
in
Combinatory
by
Tesla!
Boss
(
16.1k
points)

103
views
userisi2017
usermod
+1
vote
2
answers
22
ISI2017MMA22
The five vowels—$A, E, I, O, U$—along with $15$ $X’s$ are to be arranged in a row such that no $X$ is at an extreme position. Also, between any two vowels, there must be at least $3$ $X’s$. The number of ways in which this can be done is $1200$ $1800$ $2400$ $3000$
asked
Apr 25
in
Combinatory
by
Tuhin Dutta
Loyal
(
7.9k
points)

136
views
isi2017
engineeringmathematics
permutationsandcombinations
0
votes
0
answers
23
#Pigeonhole Principle Doubt
How many positive integers not exceeding 1000 are divisible by 7? So, the doubt here is why we are taking floor function while calculating this .
asked
Apr 17
in
Combinatory
by
Abhinavg
(
259
points)

49
views
pegionhole
#counting
0
votes
2
answers
24
GATE question
Q. 6 Xs has to be placed in the figure below such that each row contains at least one X. In how many ways can this be done? a) 160 b) 180 c) 170 d) 26
asked
Apr 15
in
Combinatory
by
Sachin Kumar Verma
(
49
points)

85
views
permutationsandcombinations
0
votes
0
answers
25
Combinations with 3 Jugs
You are given 3 jugs A,B and C of capacities 8, 5 and 3 liters, respectively. A is filled and B and C are empty. Total amount of water is 8 liters. How many different combinations are possible with at least one of the jug being empty or atleast one of them being full. For example $(8,0,0)$ , $(4,4,0)$ , $(5,3,0)$
[closed]
asked
Apr 15
in
Combinatory
by
Mk Utkarsh
Boss
(
12.6k
points)

74
views
permutationsandcombinations
0
votes
1
answer
26
Combinatorics
How many ways we can move from a point (a,b) to a point (i,j) in a coordinate system. Here i>a and j>b and at each step you can move to the right or in the upward direction.
asked
Apr 14
in
Combinatory
by
Kushagra Chatterjee
Loyal
(
8.2k
points)

70
views
permutationsandcombinations
engineeringmathematics
general
0
votes
0
answers
27
COMBINATRICS
NUMBER OF WAYS IN WHICH CORNER OF THE SQUARE CAN BE COLORED WITH TWO COLORS. (ITS IS PERMISSIBLE TO USE A SINGLE COLOUR ON ALL FOUR CORNER)
asked
Apr 13
in
Combinatory
by
Ismail
Junior
(
611
points)

58
views
permutationsandcombinations
testbooktestseries
discretemathematic
+1
vote
1
answer
28
COMBINATRICS
NUMBER OF WAYS WE CAN ARRAYS LETTERS OF THE WORD "TESTBOOK" SO THAT NO TWO VOWELS ARE TOGETHER IS
asked
Apr 13
in
Combinatory
by
Ismail
Junior
(
611
points)

73
views
testbooktestseries
permutationsandcombinations
discretemathematic
+1
vote
0
answers
29
Permutation of 4 Gs out of 5 Gs
Given symbols: $GGGGGAAATTTECCS$ No of ways such that exactly 4 Gs out of 5 Gs are together. I am getting$ \frac{11! × 11}{3!×3!×2!} $. Some one verify it?
asked
Apr 12
in
Combinatory
by
Jason
Active
(
1.4k
points)

117
views
permutationsandcombinations
engineeringmathematics
0
votes
1
answer
30
Kenneth Rosen, Generating Functions, Exercise  6.4 QNO33
asked
Apr 12
in
Combinatory
by
Abhinavg
(
259
points)

126
views
kennethrosen
discretemathematics
generatingfunctions
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