In 300 ways the committee can be chosen as to include exactly 3 men
Step-by-step explanation:
The general formula is [tex]C_{n,k}=\frac{n!}{(k!)(n-k)!}[/tex]
If we choose exactly 3 men, the remain 2 people of the committee must be women. So the group of 5 people will be having exactly 3 men and 2 women
The possible ways of selecting exactly 3 men is
[tex]C_{6,3} \cdot C_{6,2} = \frac{6!}{3!(6-3)!} \cdot \frac{6!}{2!(6-2)!}[/tex]
[tex]C_{6,3} \cdot C_{6,2} = \frac{6!}{3!(3)!} \cdot \frac{6!}{2!(4)!}[/tex]
[tex]C_{6,3} \cdot C_{6,2} = \frac{720}{(6)(6)} \cdot \frac{720}{2(24)}[/tex]
[tex]C_{6,3} \cdot C_{6,2} = \frac{720}{(36)} \cdot \frac{720}{48}[/tex]
[tex]C_{6,3} \cdot C_{6,2} = 20 \cdot 15[/tex] = 300 ways
