Question

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

Answer 1

You and 6 of your friends. Total of 7 people.

The answer is D.) 7! ; 5,040

Answer 2

Answer: D) 7!;5,040

Step-by-step explanation:

Given: The number of friends = 7

Permutations says that the number of different ways of arranging r objects out  of n objects is given by ;-

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

By permutations the number of different ways they can sit is given by :-

$^7P_7=\dfrac{7!}{(7-7)!}=\dfrac{7!}{0!}\\\\=7\times6\times5\times4times3\times2\times1\\\\=5,040$

Therefore, the different ways can you and six of your friends sit in your assigned seats in math class = 5,040.