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Question

Mathematics Question on permutations and combinations

The number of ways in which we can distribute n identical balls in k boxes is

A

(n+k−1)Ck−1(n+k-1)C_{k-1}

B

(n)Ck−1(n)C_{k-1}

C

(n−1)Ck−1(n-1)C_{k-1}

D

(n+k−1)Ck(n+k-1)C_{k}

E

nCknC_{k}

Answer

(n+k−1)Ck−1(n+k-1)C_{k-1}

Explanation

Solution

From the give data we can write,
The number of ways to distribute n identical balls into k distinct boxes is

The solution can be formed by using the concept of combination.(Note -Where only selection is important aspect.)

So, the number of ways to distribute n identical balls into k distinct boxes is

(n+k−1)Ck−1(n+k-1)C_{k-1} (_Ans)