Question

Three travellers arrive at a town where there are four hotels; in how many ways can they take up their quarters, each at a different hotel?

Answer 1

The first traveller has a choice of four hotels, and when he has made his choice in an one way, the second traveller has a choice of three; therefore the first two can make their choice in $4\times 3$ ways; and with any one such choice the third traveller can select his hotel in $2$ ways; hence the required number of ways is $4\times 3\times 2$ or $24$.