28 November, 19:29

# Mrs. Welch and her 5 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 the11 different boxes of cereal available (there are no two the same). In how many ways can the selections be made?

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1. 28 November, 21:21
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The selections be made in 462 ways.

Step-by-step explanation:

The number of different boxes = 11 boxes. The number of children = 5 children. Given that, no two boxes are same.

The number ways the boxes can be selected = 11! ways

⇒ 11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

The number of ways the 5 children can choose = 5! ways

⇒ 5! = 5 * 4 * 3 * 2 * 1

The ways that the selection can be made = (5 ways from 11!) / 5!

⇒ 5 ways from 11! = 11 * 10 * 9 * 8 * 7

1st children = 11 selections 2nd children = 10 selections 3 rd children = 9 selections 4 th children = 8 selections 5 th children = 7 selections

The selection can be made = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1)

⇒ 55440 / 120

⇒ 462