Question

In a giant bowl, Corey has 6 of each of the following types of fruit – apples, oranges, bananas and peaches. You can assume that all pieces of fruit are distinguishable, i.e. apples are apples, but each one is unique and can be distinguished from the others. If Corey hates peaches, in how many ways can he select three pieces of fruit that he would enjoy eating?

Answer 1

Corey can select three pieces of fruit that he would enjoy eating in 125 ways.

Step-by-step explanation:

To find the number of ways Corey can select three pieces of fruit that he would enjoy eating, we can use the concept of combinations. Corey has 6 choices for the first fruit, 6 choices for the second fruit, and 6 choices for the third fruit. Since Corey hates peaches, he cannot choose them. This means he has 5 choices for each of the three fruits he selects. To find the total number of ways, we multiply the number of choices for each fruit: 5 x 5 x 5 = 125 ways.