Question

In how many ways, a committee consisting of 4 boys and 3 girls can be formed from a group of 15 boys and 10 girls?
1. 172800
2. 163800
3. 327600
4. 152800

Answer 1

Correct Answer - Option 2 : 163800

Given:

Number of boys = 15

Number of girls = 10

Concept used:

For the selection r objects from n objects,

nCr = n!/{(r!)(n - r)!}

Calculation:

The number of ways for selecting 4 boys from 15 boys = 15C4

⇒ The number of ways for selecting 3 girls from 10 girls = 10C₃

⇒ Total number of ways a committee consisting of 4 boys and 3 girls = 15C4 × 10C3

⇒ The total number of ways a committee consisting of 4 boys and 3 girls = [(15 × 14 × 13 × 12 × 11!)/(4!)(11!)] × [(10 × 9 × 8 × 7!)/(3!)(7!)]

⇒ The total number of ways a committee consisting of 4 boys and 3 girls = 1365 × 120 = 163800

∴ The total number of ways a committee consisting of 4 boys and 3 girls is 163800.