A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose:(a) 27 candies?

The problem you're describing is a classic example of a problem in combinatorics, specifically a problem of combinations with repetition.

This type of problem is solved using the formula for combinations with repetition, which is:

C(n + r - 1, r)

where n is the number of types of items (in this case, types of candies), and r is the number of items to choose (in this case, candies).

So, for your problem, n = 5 (cherry, strawberry, orange, lemon, pineapple) and r = 27 (the number of candies to choose).

Plugging these values into the formula gives:

C(5 + 27 - 1, 27) = C(31, 27)

This is a combination calculation, which can be calculated as:

C(31, 27) = 31! / [(31-27)! * 27!]

where "!" denotes factorial, which is the product of all positive integers up to that number.

So, the number of ways to choose 27 candies from 5 types is the result of this calculation.