Question

Mrs. Welch and her 6 children are shopping at a local grocery store. Each of the children will be allowed to select one box of cereal for their own from the 8 different boxes of cereal available​ (there are no two the​ same). In how many ways can the selections be​ made?

Answer 1

If you are only asking the selections combinations, it would be 8x7/2=28.

If the selections are to be matched with the child, it would be 8x7x6x5x4x3=20160

Answer 2

Answer: 20160

Explanation:

Given: The number of different boxes of cereal available​ = 8

The number of children are shopping at a local grocery store =6

Since, each of the children will be allowed to select one box of cereal for their own from the 8 different boxes of cereal available​ and there are no two the​ same.

Then by using permutation, the number of ways the selections can be​ made is given by :-

`^8P_6=(8!)/((8-6)!)=(8*7*6*5*4*3*2!)/(2!)=20160`

Hence, the number of ways the selections can be​ made = 20160