a group consists of 8 freshmen and 7 sophomores how many way

a group consists of 8 freshmen and 7 sophomores. how many ways can you select a committee of 5 from the group? how many ways can one select a committee of 3 freshmen and 2 sophomores?

Solution

Total number of person = 8+7=15.

From 15 persons, 5 persons can be selected in 15C5 ways =3003 ways (answer)

From 8 freshmen, 3 freshmen can be selected in 8C3 ways and from 7 sophomores , 2 sophomores can be selected in 7C2 ways= 21 ways . So total number of ways = 3003*21=63063 ways (answer)