A hint to get started
Count restricted committees using cases and complements
A class consists of 8 girls and 10 boys. How many committees of 4 can be formed if
(i) there are no restrictions,
(ii) the committee has at most 1 boy,
(iii) the committee must have at least 1 girl,
(iv) Boy A or Girl B must be in the committee?
CJC · Lecture · Example 8
Decide whether order matters and repetition is allowed; then count stages or disjoint cases.