Question

There are nine empty seats in a theater, and six customers need to find places to sit. How many different ways can these six seat themselves?

Answer 1

Answer: 60480

Explanation:

Given : The number of empty seats in a theater = 9

The number of customers need to find places to sit =6

Since order matters here, so we use permutations

The permutations of n things taking r at a time is given by :-

`^nP_r=(n!)/((n-r)!)`

Then, the number of ways to arrange 6 seat in 9 seats :-

`^9P_6=(9!)/((9-6)!)=(9*8*7*6*5*4*3!)/(3!)\\\\=60480`

Hence, the number of ways to arrange 6 seat in 9 seats = 60480