How many ways can I select 5 pieces of fruit from apples, oranges, strawberries and pears (I have at least 5 of each)?

the 20 pieces allow you to select all of one kind, or any combination

20C5

To find the number of ways to select 5 pieces of fruit, we can use the concept of combinations. In this case, we have 4 types of fruit: apples, oranges, strawberries, and pears. Since we have at least 5 of each fruit, we can consider the combination of selecting 5 fruits from each type.

To calculate the combination, we can use the formula for combinations:

C(n, r) = n! / (r!(n - r)!)

where n is the total number of objects (in this case, the total number of fruit types, which is 4), and r is the number of objects chosen (in this case, 5).

Let's calculate the combinations step by step:

1. Calculate the factorial of n (4!):
4! = 4 x 3 x 2 x 1 = 24

2. Calculate the factorial of r (5!):
5! = 5 x 4 x 3 x 2 x 1 = 120

3. Calculate the factorial of (n - r) (4 - 5!):
(4 - 5)! = (4 - 5) x (4 - 4)! = (-1) x 1 = -1 (factorial of a negative number is not defined).

4. Plug the values into the combination formula:
C(4, 5) = 4! / (5!(4 - 5)!)
= 24 / (120 x -1)

Since the factorial of -1 is not defined, the number of ways to select 5 pieces of fruit is 0.

Therefore, there are no ways to select exactly 5 pieces of fruit from the given types of fruit.