Question

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

Answer 1

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+3-1C_3-1 = ⁷C₂ = 21

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