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

Step-by-step 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 :-

$^nP_r=\dfrac{n!}{(n-r)!}$

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

$^9P_6=\dfrac{9!}{(9-6)!}=\dfrac{9\times8\times7\times6\times5\times4\times3!}{3!}\\\\=60480$

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