How many ways can 5 passengers be accommodated in a 6-seater boat?

1) Any of 5 passengers can take the first seat – 5 ways.
2) Any of the 4 remaining passengers can take the second seat – 4 ways.
3) Any of the 3 remaining passengers can take the third place – 3 ways.
4) Any of the 2 remaining passengers can take the fourth seat – 2 ways.
5) The only remaining passenger will sit in fifth place – 1 way.
6) The sixth place will remain empty.
But any of the 6 places can remain empty, which means 6 more ways.

It turns out in total
6 * 5 * 4 * 3 * 2 * 1 = 6! = 720 (ways).