# Explain the difference between a permutation and a combination of n items taken r at a time.

Question
Asked Dec 19, 2019
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Explain the difference between a permutation and a combination of n items taken r at a time.

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## Expert Answer

Step 1

Two types of counting problems occur so frequently that they deserve special

attention. These problems are as follows:

(1) How many different arrangements (ordered lists) of r objects can be formed from a set of n distinct objects?

(2) How many different selections (unordered lists) of r objects can be made from a set of n distinct objects?

Permutation can be used for Type (1) and combination can be used for Type (2).

Step 2

An arrangement or ordering of n distinct objects is called a permutation of the objects. The number of permutation of n objects is n!. And the number of ways to arrange r objects that are taken from n objects is nPr. here

Step 3

If r <= n, then an unordered selection of r objects chosen from a set of n distinct objects is called an r-combination of the objects...

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