Question

A cake shop has plain cakes, cherry cakes, chocolate cakes, and apple cakes. How many ways are there to choose

1, ten cakes with at least one of each kind?

2, ten cakes with at least four apple cakes and no more than one chocolate cake ?

Answer 1

1. 10C4 = 210

2. 4C1 + 10C1 = 14

Explanation:

There are total 4 types of cakes available. Chocolate, cherry, apple and plain cakes. If we select 10 cakes, the possibility that at least 1 cake is selected for every variant is 210. We use computation technique in statistics for this purpose 10C4. After calculation we get 210.

If we select 4 apple cakes and one chocolate cake then there will be 14 different ways to do this. It is assumed that the order does not matter.