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Recent questions tagged balls-in-bins

17 votes

3 answers

1

GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .

Arjun asked in Combinatory Feb 15, 2022

by Arjun

10.2k views

2 votes

2 answers

2

ISI2017-DCG-28
A basket contains some white and blue marbles. Two marbles are drawn randomly from the basket without replacement. The probability of selecting first a white and then a blue marble is $0.2$. The probability of selecting a white marble in the first draw is $0.5$. What is the ... blue marble in the second draw, given that the first marble drawn was white? $0.1$ $0.4$ $0.5$ $0.2$

gatecse asked in Probability Sep 18, 2019

912 views

5 votes

2 answers

3

CMI2018-A-7
Let $C_{n}$ be the number of strings $w$ consisting of $n$ $X's$ and $n$ $Y's$ such that no initial segment of $w$ has more $Y's$ than $X's.$ Now consider the following problem. A person stands on the edge of a swimming pool holding a bag of $n$ red and $n$ blue ... $\frac{C_{n}}{\binom{2n}{n}}$ $\frac{n\cdot C_{n}}{(2n)!}$ $\frac{n\cdot C_{n}}{\binom{2n}{n}}$

gatecse asked in Probability Sep 13, 2019

584 views

19 votes

4 answers

4

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? $3^{35}$ $3^{50}-2^{50}$ $\binom{35}{2}$ $\binom{50}{15} \cdot 3^{35}$ $\binom{37}{2}$

go_editor asked in Combinatory Dec 21, 2016

4.1k views

32 votes

4 answers

5

TIFR CSE 2015 | Part A | Question: 8
There is a set of $2n$ people: $n$ male and $n$ female. A good party is one with equal number of males and females (including the one where none are invited). The total number of good parties is. $2^{n}$ $n^{2}$ $\binom{n}{⌊n/2⌋}^{2}$ $\binom{2n}{n}$ None of the above

makhdoom ghaya asked in Combinatory Dec 5, 2015

by makhdoom ghaya

4.0k views

22 votes

5 answers

6

TIFR CSE 2013 | Part A | Question: 9
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^{n} . n!}$ $\frac{n!}{2}$ None of the above

makhdoom ghaya asked in Combinatory Nov 4, 2015

by makhdoom ghaya

3.3k views

24 votes

6 answers

7

TIFR CSE 2012 | Part A | Question: 7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $\frac{n!}{2}$ None of the above

makhdoom ghaya asked in Combinatory Oct 26, 2015

by makhdoom ghaya

4.6k views

43 votes

11 answers

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GATE IT 2004 | Question: 35
In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,\ldots 5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$

Ishrat Jahan asked in Combinatory Nov 2, 2014

by Ishrat Jahan

11.4k views

23 votes

9 answers

9

GATE CSE 2003 | Question: 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 $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$

Kathleen asked in Combinatory Sep 16, 2014

11.2k views

34 votes

8 answers

10

GATE CSE 2002 | Question: 13
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, the number of ways is $2$, i.e., $1+2, 2+1$. Give only ... $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.

Kathleen asked in Combinatory Sep 15, 2014

7.2k views

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