Question

A committee of six Congressmen will be selected from a group of eight Republicans and four Democrats. Find the number of ways of obtaining a committee with exactly three Republicans.

Answer 1

224

Explanation:

Given that a committee of six Congressmen will be selected from a group of eight Republicans and four Democrats.

Total no of ways of selecting 6 persons from the given list

= taking 6 persons out of 12 persons

=
`12C6\\=924`

Favourable ways

= ways of selecting 3 republicians

= 3 republicians and 3 democrats

=
`8C3(4C3)\\= 4(56)\\\\=224`

the number of ways of obtaining a committee with exactly three Republicans.

= 224