Question

A committee of 10 members has to be formed from 15 men and 7 women. In how many ways can this be done when the committee consists of at least 6 women?
1. 10011
2. 10010
3. 11010
4. 12740

Answer 1

Correct Answer - Option 2 : 10010

Given : A committee of 10 members should consists of at least 6 women. 

Number of persons: 15 men and 7 women. 

Total number of ways = ⁷C₆ × ¹⁵C₄+ ⁷C₇ × ¹⁵C₃

We know that,

The formula used here is:

 \(^nC_r = \frac{n!}{k!(n-k)!}\)

Applying this formula in the above equation:

Total number of ways = \( \frac{7!}{6!(1)!} × \frac{15!}{4!(11)!} + \frac{7!}{7!(0)!}× \frac{15!}{3!(12)!}\) 

→ \(7 × \frac{15×14×13×12}{4 ×3×2} +1× \frac{15×14×13}{3×2}\) 

→ 7 × 1365 + 455

→ 9555 + 455

→ 10010

Hence, 10010 is the correct answer.