If a manufacturer is trying to put together a sample collection of her safetyproduct and order is not important, how many combinations can becreated with 15 items that will be placed in packages containing fiveitems? If order is important, how many permutations can be created?

Question
Asked Feb 26, 2019
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If a manufacturer is trying to put together a sample collection of her safety
product and order is not important, how many combinations can be
created with 15 items that will be placed in packages containing five
items? If order is important, how many permutations can be created?

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Expert Answer

Step 1

Find the number of ways in which 15 items can be placed in packages containing 5 items without giving importance to order.

The total number of items is 15.

The number of items that have to be packed in each package is 5.

Here, it is given that order is not important. That is, 15 items can be placed in packages containing 5 items in any order.

Since, the order is not important, combinations rule is used to obtain the number of ways in which 15 items can be placed in packages containing 5 items.

The number of different ways in which 15 items can be placed in packages containing 5 items without giving importance to order is obtained as 3,003 from the calculation given below:

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Step 2

Find the number of ways in which 15 items can be placed in packages containing 5 items in a specific order.

Here, it is given that 15 items has to be placed in packages containing 5 items in a specific order.

Arrangement of the elements in a specific order is known as permutation. Here, among 15 items, 5 items has to be packed in each package and their arrangement has to be done within the 5 positions. Therefore...

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