Answer: 210 ways
Step-by-step explanation:
We know that the combination of n things taking m at a time is given by :-
[tex]^nC_m=\dfrac{n!}{m!(n-m)!}[/tex]
Now, the number of ways can a committee of five men and four women be formed from a group of six men and seven women :-
[tex]^6C_5\times ^7C_4\\\\=\dfrac{6!}{5!(6-5)!}\times\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{6\times5!}{5!1!}\times\dfrac{7\times6\times5\times4!}{4!3!}=6\times35=210[/tex]
Hence, there are 210 ways to form a committee of five men and four women from a group of six men and seven women .
