Question

The number of ways in which $11$ identical apples can be distributed among $6$ persons so that each person get at least one apple is

• A. $250$
• B. $252$
• C. ${}^{16}{\text{C}}_5$
• D. ${}^{11}{\text{C}}_6$

Answer 1

Answer: (B)

$252$

Distribution of m identical objects to n persons so that each gets at least one will be

${}^{m-1}{C}_{n-1}$

Here $m=11$ and $n=6$.

Hence, by substituting, we get

${}^{10}{C}_5$

$=\frac{10!}{5!.5!}$

$=252$