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)!}](https://tex.z-dn.net/?f=%5EnP_r%3D%5Cdfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
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](https://tex.z-dn.net/?f=%5E9P_6%3D%5Cdfrac%7B9%21%7D%7B%289-6%29%21%7D%3D%5Cdfrac%7B9%5Ctimes8%5Ctimes7%5Ctimes6%5Ctimes5%5Ctimes4%5Ctimes3%21%7D%7B3%21%7D%5C%5C%5C%5C%3D60480)
Hence, the number of ways to arrange 6 seat in 9 seats = 60480
Answer:
No
Step-by-step explanation:
Two consecutive sides means that the two sides are connected in a shape by a vertex. If the sides were parallel, they would have to be right on top of each other, so two consecutive sides cannot be parallel.