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This question is from the GRE math:

A group of 4 people are standing in a straight line. In how many different ways can these people be standing on the line?

The answer is $24$. If the permutations formula is this, how did they derive this answer? Thanks.

$$\frac{n!}{(n-r)!}$$

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    $\begingroup$ The number of permutations on $n$ objects is $n!$ $\endgroup$ – Seth Apr 28 '14 at 20:59
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Any of the $4$ people can be the first person. Then, there are $3$ remaining choices for the second person, then $2$ remaining choices for the third, and then the fourth has been decided.

Hence, there are $n!$ possible ways.

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