Question

In how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively

Answer 1

2520 ways

Explanation:

Given

`n = 10`

`r = (2,3,5)`

Required

The number of selection

First, select 2 people from 10 in 10C2 ways.

There are 8 people, left.

Next, select 3 people from 8 in 8C3 ways.

There are 5 people left.

Lastly, select 5 from 5 in 5C5 ways

So, we have:

`Total = ^(10)C_2 * ^8C_3 * ^5C_5`

Using combination formula

`Total = 45 * 56 * 1`

`Total = 2520`