Question

A committee of 8 students is to be selected from 8 boys and 6 girls. In how many ways this can be done if each group is to consist of at least 3 boys and 3 girls.

Answer 1

The total number possible ways = 2506

Total number of boys = 8

Total number of girls = 6

In each selected group there must be atleast 3 boys and 3 girls in a 8 member group .

Case 1 -

Boys = 5 , girls = 3

We will select 5 boys from total boys and 3 girls from total girls -

=> 8C5 × 6C3

=> 56 × 20

=> 1120

Case 2-

Boys = 3 , girls = 5

We will select 3 boys from total boys and 5 girls from total girls -

=> 8C3 × 6C5

=> 56 × 6

=> 336

Case 3-

Boys = 4 , girls = 4

We will select 4 boys from total boys and 4 girls from total girls -

=> 8C4 × 6C4

=> 70 × 15

=> 1050

Total number of ways = sum of all three cases

= 1120 + 336 + 1050

= 2506