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Recent questions tagged combinatory

3 votes
1 answer
874
combinatorics
coefficient of x^20 in (1+x+x^2+......................)^2 is?
coefficient of x^20 in (1+x+x^2+......................)^2 is?
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2 votes
1 answer
875
Stars and bar problem
Can someone explain stars and bar problme using suitable example and images Problem : https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29#Proofs_via_the_method_of_stars_and_bars
Can someone explain stars and bar problme using suitable example and imagesProblem : https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29#Proofs_via_the_metho...
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4 votes
2 answers
876
Stack Permutation
Which of the following permutations can be obtained in the output (in the same order) using a stack assuming that the input is the sequence 5, 7, 8, 4, 6 in that order? a)6, 8, 4, 7, 5 b)6, 4, 5, 7, 8 c)6, 4, 7, 8, 5 d)7, 8, 4, 6, 5
Which of the following permutations can be obtained in the output (in the same order) using a stack assuming that the input is the sequence 5, 7, 8, 4, 6 in that order?a)...
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4 votes
1 answer
877
test series counting
The number of pairs of set (X, Y) are there that satisfy the condition X, Y ⊆ {1, 2, 3, 4, 5, 6} and X ∩ Y = Φ ________.
The number of pairs of set (X, Y) are there that satisfy the condition X, Y ⊆ {1, 2, 3,4, 5, 6} and X ∩ Y = Φ ________.
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2 votes
1 answer
878
Number of ways ... distinguishable into distinguishable.
How many ways can n books be placed on k distinguishable shelves if no two books are same and the position of the books on the shelves matter.
How many ways can n books be placed on k distinguishable shelves if no two books are same and the position of the books on the shelves matter.
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1 votes
1 answer
879
TheTrevTutor discrete maths 2 videos
I want to know how good are the videos of discrete maths by TheTrevTutor. Has anyone been following the videos while preparing for GATE? https://www.youtube.com/watch?v=DBugSTeX1zw&list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
I want to know how good are the videos of discrete maths by TheTrevTutor. Has anyone been following the videos while preparing for GATE? https://www.youtube.com/watch?v=D...
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3 votes
1 answer
880
Combinatorics
The answer given is n-k+1C2 but couldn't understand how both are related
The answer given is n-k+1C2 but couldn't understand how both are related
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0 votes
1 answer
882
combinations
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4 votes
2 answers
888
Generating function
Find $\large\color{maroon}{a^n}$ for the following generating function, $\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$ $\large\color{maroon}{a^n}$ = closed form of the $nth$ term in the corresponding sequence.
Find $\large\color{maroon}{a^n}$ for the following generating function,$$\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$$$\large\color{maroon}{a^n}$ = closed...
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6 votes
1 answer
889
Generating function
What is the coefficient of $\large\color{green}{x^{6}}$ in the following series expansion? $\color{maroon}{\begin{align*} \frac{1}{1-x}.\frac{1}{1-x^2}.\frac{1}{1-x^3}........ \end{align*}}$
What is the coefficient of $\large\color{green}{x^{6}}$ in the following series expansion?$$\color{maroon}{\begin{align*} \frac{1}{1-x}.\frac{1}{1-x^2}.\frac{1}{1-x^3}......
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15 votes
2 answers
890
TIFR CSE 2017 | Part A | Question: 6
How many distinct words can be formed by permuting the letters of the word $\text{ABRACADABRA}?$ $\frac{11!}{5! \: 2! \: 2!}$ $\frac{11!}{5! \: 4! }$ $11! \: 5! \: 2! \: 2!\:$ $11! \: 5! \: 4!$ $11! $
How many distinct words can be formed by permuting the letters of the word $\text{ABRACADABRA}?$$\frac{11!}{5! \: 2! \: 2!}$$\frac{11!}{5! \: 4! }$$11! \: 5! \: 2! \: 2!\...
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19 votes
4 answers
891
TIFR CSE 2017 | Part A | Question: 5
How many distinct ways are there to split $50$ identical coins among three people so that each person gets at least $5$ coins? $3^{35}$ $3^{50}-2^{50}$ $\binom{35}{2}$ $\binom{50}{15} \cdot 3^{35}$ $\binom{37}{2}$
How many distinct ways are there to split $50$ identical coins among three people so that each person gets at least $5$ coins?$3^{35}$$3^{50}-2^{50}$$\binom{35}{2}$$\bino...
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4 votes
3 answers
893
Number of solutions
Number of non negative integer solutions to the equation X1 + X2 + X3 + X4 = 15, where $1 \leqslant X1,X2,X3,X4 \leqslant6$ is ________
Number of non negative integer solutions to the equation X1 + X2 + X3 + X4 = 15, where $1 \leqslant X1,X2,X3,X4 \leqslant6$ is ________
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0 votes
1 answer
897
permutation
number of arrangements in which 5 boys and 3 girls are arranged such that at least 2 girls to be separated
number of arrangements in which 5 boys and 3 girls are arranged such that at least 2 girls to be separated
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1 votes
1 answer
898
sheldon Ross
A coin is flipped n times. Assuming that the flips are independent, with each one coming up heads with probability p, what is the probability that there is a string of k consecutive heads?
A coin is flipped n times. Assuming that the flips are independent, with each onecoming up heads with probability p, what is the probability that there is a string of kco...
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3 votes
2 answers
899
Permutation and combination
The number of ways can 10 balls be selected from urn contain 10 identical red balls 5 identical green balls and 3 identical blue balls ?
The number of ways can 10 balls be selected from urn contain 10 identical red balls 5 identical green balls and 3 identical blue balls ?
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