Question

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

Answer 1

Answer: 840

Step-by-step explanation:

Given : The total number of empty seats in the theater = 7

The number of customers need to find places to sit = 4

Since here order of their sitting matters , then we use permutation to find the number of ways of sitting.

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

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

Then , the number of permutations of 7 things taking  at a time is given by :-

$^7P_4=\dfrac{7!}{(7-4)!}\\\\=\dfrac{7\times6\times5\times4\times3!}{3!}=840$

Hence, the number of different ways can these four seat themselves = 840