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A committee consisting of 7 boys and 2 girls can be formed from a group of 11 boys and 10 girls, By how many ways it can be selected?
1. 14850
2. 14950
3. 14960
4. 13850

1 Answer

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Correct Answer - Option 1 : 14850

Given:

A committee having 7 boys and 2 girls

A group consist 11 boys and 10 girls

Formula used:

Combination = n! / r!(n - r)!

Calculation:

A committee having 7 boys and 2 girls

A group consist 11 boys and 10 girls

Combination = n! / r!(n - r)!

The number of ways it can be selected = {n! / r!(n - r)!} × {n! / r!(n - r)!}

⇒ {11! / (7! × 4!)} × {10! / (2! × 8!)}

⇒ {(11 × 10 × 9 × 8) / (4 × 3 × 2)} × {(10 × 9) / (2)}

⇒ 330 × 45

⇒ 14850 

∴ The number of ways it can be selected is 14850.

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