When selecting from multiple groups with constraints, break into cases based on the constraint. Example: select 5 from 4 boys and 3 girls with at least 2 boys and 1 girl. Cases: (2B,3G), (3B,2G), (4B,1G). Calculate each: C(4,2)*C(3,3) + C(4,3)*C(3,2) + C(4,4)*C(3,1) = 6 + 12 + 3 = 21. Check: sum should not exceed C(7,5) = 21.