Question

The number of ways that 30 mangoes can be distributed among 5 boys if each boy is eligible for any number of mangoes is​

Answer 1

Given:

30 mangoes being distributed among 5 boys.

To Find:

The number of ways that 30 mangoes can be distributed among 5 boys if each boy is eligible for any number of mangoes is​?

Solution:

Here, it is given that - 30 mangoes are given which are being distributed among 5 boys.

Implies, 30 mangoes are identical.

Since, we know that-

Number of ways of distributing n identical things among r persons is

$= \[{}^{n + r - 1}{C_{r - 1}}\]$

Hence, the number of ways that 30 mangoes can be distributed among 5 boys if each boy is eligible for any number of mangoes is $\[{}^{30 + 5 - 1}{C_{5 - 1}} = {}^{34}{C_4}\]$ .