Question

Four visitors $A,B,C$ and $D$ arrive at a town which has $5$ hotel.In how many ways can they disperse themselves among $5$ hotels ,if hotels are used to accommodate them ? No two visitors can go to the same hotel.

Answer 1

Given,

Number of visitors= $4$

Number of hotels= $5$

So, $A$ can disperse among $5$ hotels,

$B$ can disperse among $4$ hotels,

$C$ can disperse among $3$ hotels,

$D$ can disperse among $2$ hotels.

$\therefore$ They can disperse in the hotels in $5\times 4\times 3\times 2=120$ ways.