Math Question, (Help Needed with explanation)

Question

1.Q;In a class there are five girls and seven boys. For a school project

the teacher would like to form a group of three students.

What are the chances that there will be at least one female in the group?

Answer 1

You can choose the students in C (12, 3) ways

Ways with only boys C (7,3)

Ways with at least one girl C (12,3) - C (7,3)

So probability = [ C(12,3) - C(7,3) ] / C (12,3)