We must choose a 5-member team from 12 girls and 10 boys. How many ways are there to make the choice so that there are no more than 3 boys on the team?
The correct answer is (22 choose 5) - (12 choose 1)(10 choose 4) - (10 choose 5).
I understand the (22 choose 5) part, but where I am confused at is the other two parts. I do not know how to get those parts.. Can anyone help me understand how to get to the solution?