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 :-
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Then, the number of ways to arrange 6 seat in 9 seats :-
[tex]^9P_6=\dfrac{9!}{(9-6)!}=\dfrac{9\times8\times7\times6\times5\times4\times3!}{3!}\\\\=60480[/tex]
Hence, the number of ways to arrange 6 seat in 9 seats = 60480
