In how many ways can 6 people be lined up to get on a bus?

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In how many ways can 6 people be lined up to get on a bus?

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Answer 1 · 2016-01-27T11:28:52

$6! = 720$ $6! = 720$

Explanation:

$6$ $6$ choices for the first person;
$XX$ $color(white)("XX")$ for each of these, $5$ $5$ choices for the next;
$XXXX$ $color(white)("XXXX")$ for each of these, $4$ $4$ choices for the next;
$XXXXXX$ $color(white)("XXXXXX")$ for each of these, $3$ $3$ choices for the next;
$XXXXXXXX$ $color(white)("XXXXXXXX")$ for each of these, $2$ $2$ choices for the next;
$XXXXXXXXXX$ $color(white)("XXXXXXXXXX")$ for each of these, $1$ $1$ choice for the last person.

$6 \times 5 \times 4 \times 3 \times 2 \times 1 = 6! = 720$ $6xx5xx4xx3xx2xx1 = 6! = 720$

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In how many ways can 6 people be lined up to get on a bus?

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