A cafeteria has 3 meat selections, 4 vegetable selections and 5 dessert selections. Johnny, who has a sweet tooth, will choose a meal consisting of 1 meat selection, 2 vegetable selections (his mother made him do it) and 2 dessert selections. How many different meals can Johnny create? Keep in mind that Johnny may like a dessert so much that he may choose two portions of the same dessert, but he would never select two portions of any single vegetable. [Show work, the answer alone will not get much credit]
Solution: If Johnny chooses two different desserts then the number of meals is C(3,1)* C(4,2)*C(5,2) = (3)(6)(10) = 180
but if he chooses identical desserts the number of meals is
C(3,1)*C(4,2)*5 = (3)(6)(5) = 90,
so the total number of meals that Johnny could create is 180 + 90 = 270.