Question

In how many ways 10 mangoes can be distributed among 4 persons if any person can get any number of mangoes?

• A. $26\times 11$
• B. $13\times 132$
• C. $13\times 14$
• D. ${}^{13}{C}_3$

Answer 1

Answer: (A)

$26\times 11$

Required number of ways

Let $n$ be the number of mangoes, then ${n+r-1}_{C_{r-1}}={10+4-1}_{C_{4-1}}={13}_{C_3}$

and $r$ be the number of children.

${13}_{C_3}=\frac{13!}{3!(13-3)!}$

$=\frac{13!}{3!10!}$

$=\frac{13\times 12\times 11\times 10!}{3\times 2\times 1\times 10!}$

$=\frac{13\times 12\times 11}{3\times 2}=26\times 11=286$