1. ## number of ways

How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men

2. Originally Posted by write2rvr
How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men
2W 3M + 3W 2M + 4W 1M = $^{10}C_2 \cdot ^{15}C_3 + ^{10}C_3 \cdot ^{15}C_2 + ^{10}C_4 \cdot ^{15}C_1 = \, ....$

3. Originally Posted by write2rvr
How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men
Containing 2 women and 3 men : $10C2\times15C3=20475$
Containing 3 women and 2 men : $10C3\times15C2=12600
$

Containing 4 women and 1 man : $10C4\times15C1=3150$
Total choices $=36225$