Problem 1161

Is the selection a permutation, a combination, or neither?

Ten woman in a salon are dying their hair blonde, brunette, black, or red.

 

Solution:-

 

Use the definitions of permutation and combination to decide the type of selection mode.

A permutation of a set of n distinct is an arrangement of the objects in a specific order without repetition.

A combination of a set of n distinct object is an arrangement of the object without repetition where order is irrelevant.

In the selection process of the problem, the order of who gets their hair dyed and the order that the colors are chosen is not important.

There is repetition since there are only four hair colors to choose from and 10 women dying their hair.

Use the fact that the selection process has repetition and order is irrelevant to determine the type of selection.

The selection is neither a permutation or a combination.

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