Question

In how many ways can 6 bicycles be parked in a row?

Answer 1

`6` bicycles can be parked in a row in `6! =720` ways.

Explanation:

Assuming the bicycles are distinguishable

there are `6` choices for the first bike;

and for each of these `6` choices there remain `5` choices for the second bike (giving `6xx5=30` choices for the first two bikes);

and for each of these `6xx5` choices there remain `4` choices for the third bike (giving `6xx5xx4=120` choices for the first `3` bikes);

and for each of these `6xx5xx4` choices there remain `3` choices for the fourth bike (giving `6xx5xx4xx3=360` choices for the first `4` bikes);

and for each of these `6xx5xx4xx3` choices there remain `2` choices for the fifth bike (giving `6xx5xx4xx3xx2=720` choices for the first `5` bikes);

and for each of these `6xx5xx4xx3xx2` choices there remains `1` choices (really no choice) for the sixth bike (giving `6xx5xx4xx3xx2xx1=720` choices for the `6` bikes);

Notation: `6xx5xx4xx3xx2xx1` can be written as `6!` (read as "six factorial").