Question

in how many ways can a committee of three men and four woman be formed from a group of twelve men and twelve woman

Answer 1

Number of ways to of forming 3 men from 12 men $= \frac{12!}{3!(12-3)!} = \frac{10 \times 11 \times 12}{2 \times 3} = 220$

Number of ways to of forming 4 woman from 12 woman $= \frac{12!}{4!(12-4)!} = \frac{9 \times 10 \times 11 \times 12}{2 \times 3 \times 4} = 495$

Number of ways of forming a committee of three men and four woman $= 220 \times 495 = 108900 \;ways$