Question

A class consists of 12 boys and 8 girls. In how many ways can a committee of 6 be formed if:
there must be at least 1 boy and 1 girl?
I got 896 at the end but not sure if it is right.

Answer 1

no boys ... 8C6 = 28

no girls ... 12C6 = 924

any combination ... 20C6 = 38760

at least one of each ... 38760 - 924 - 28 = ?