Write the number of permutations in factorial form. Then simplify. How many different ways can you and six of your friends sit in your assigned seats in math class?
A. 6!; 120
B. 6!; 720
C. 7!; 2,520
D. 7!; 5,040
The answer is B.
There are 6 friends who can sit in any of the 6 seats, so the initial number of permutations is 6!. However, since the order of the friends doesn't matter (i.e. AB is the same as BA), we need to divide by the number of ways to arrange those 6 friends, which is another 6!.
So our calculation is (6!)/(6!) = 1, which simplifies to 6! = 720.