Question

Suppose that a cookie shop has three different kinds of cookies. How many different ways can...

Suppose that a cookie shop has three different kinds of cookies. How many different ways can five cookies be chosen?

Number of cookies to be chosen, n = 5

And, total variety of cookies are 3. Suppose, there are 3 types of cookies, A, B & C.

Suppose, we choose x cookies of type A, y cookies of type B & z cookies of type C.

Then, we need to find all possible non-negative integral solutions of, x + y + z = 5

The number of non-negative integral solutions of the equation is,  5+3-1C3-1 = 7C2 = 21

So, there are 21 different ways to choose five cookies from the lot.

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