Four visitors A, B, C, D arrived at a town that has 5 hotels. In how many ways, can the disperse themselves among 5 hotels.

Answer

120

Explanation

Four hotels can be chosen out of five hotels in `.^(5)C_(4)` ways and the four visitors can stay in one of four hotels in 4! Ways (one visitor in one hotel).
Therefore, the total number of ways of accommodating the visitors is ` .^(5)C_(4)xx4!=5xx24=120`.