Question

A committee of 5 students is to be choosen from 6 boys and 4 girls .probability that it has only 2 girls

Answer 1

A committee of 5 students is to be choosen from 6 boys and 4 girls .probability that it has only 2 girls

so, committee should contains 2 girls and 5-2 = 3 boys

2 girls are selected from 4 girls
so, no of ways of selecting 2 girls = 4C2
$4C2 = \frac{4 \times 3}{2 \times 1} = 2 \times 3 = 6 \: ways$
3 boys are selected from 6 boys
so, no of ways of selecting 3 boys = 6C3
$6C3= \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 5 \times 4 = 20 \: ways$
selecting 5 members from 10 students
so, no of selecting 5 members = 10C5
$10C5 = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} = 2 \times 9 \times 2 \times 7 = 252 \: ways$
probability of selecting 2 girls and 3 boys = (4C2 × 6C3)/(10C5) = (6×20)/252 = 10/21