A class has 10 boys and 12 girls In how many ways can a comm

A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls?

Solution

So, the number of ways are as follows:

0 girls 4 boys : ¹²C₀ * ¹⁰C₄ = 210 ways

1 girl, 3 boys : ¹²C₁ * ¹⁰C₃ = 1440 ways

2 girls, 2 boys : ¹²C₂ * ¹⁰C₂ = 2970 ways

Total number of ways = 4620 ways

Hope this helps.