Question

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls ? (ii) atleast 3 girls ?

Answer 1

1)  A committee consisting of 3 girls and 4 boys can be formed in ¹C₃×⁹C₄ ways

⇒⁴C₁×⁹C₄

⇒4/1×9×8×7×6/1.2.3.4

⇒504 ways

2) Since, the committee requires 7 members and it must have at least 3 girls means the committee can consist 3 or more number of girls.
This can be done in two ways, i.e., select 3 girls from 4 or all the 4 girls.
By the principles of combination, we can select 4 boys from 9 and 3 girls from the 4 or also 3 boys and 4 girls.
This can be computed as total (9C4 * 4C3) + (9C3 * 4C4) ways