Question

If a group consists of 8men and 6women. in how many ways a committee of 5people be selected if there must be at least one man. If there must be at least one of each sex

Answer 1

at least 1 man means there are 7 men and 6 women (13 people) to select the other 4. So, 13C4 = 13! / (4!9!) = 715. Since there are 8 ways to pick the first man, that makes 8*715 = 5720 ways in all.
now you try the other one.