A teacher wishes to choose a group of students to help with a presentation. If he needs 2 boys and 3 girls to help with the project and has 14 boys and 12 girls in his classroom, in how many ways can he
make the selection?

20020 ways

Choosing 2 boys can be done in 14 x 13 = 182 ways.
But this puts them in order ( first and second) which is not required so the unordered number ways is 182 / 2 = 91
Choosing 3 girls can be done in 12 x 11 x 10 = 1320 ways but 3 girls can appear in 3! ways = 6.
The number of unordered selections of 3 girls = 1320 / 6 = 220
The total number of selections is 91 x 220 = 20020.

If you thought the answer was 240240 it is because you used permutations rather than combinations.

If you are still confused, remember choosing Alan and Bruce is the same as choosing Bruce and Alan.
For the girls you could choose CDE, CED, DCE, DEC, ECD OR EDC and still get exactly the same 3 girls.