SOLUTION: 10 people line up for a photo, including you and your friend. How many line arrangements are there if the photographer insists on keeping 3 people in between you and your friend?

Question 352388: 10 people line up for a photo, including you and your friend. How many line arrangements are there if the photographer insists on keeping 3 people in between you and your friend?
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
There are 10 people: A(you), B(your friend) and 8 others.

You and your friend are spaced like this:
A____B or B____A = two ways

Select 3 of the Others and arrange them in the spaces.

There are: 8P3 = 8!/5! = 336 ways.

Now we have 6 "people" to arrange: AxyzB and 5 others.

There are: 6! = 720 ways.

Therefore, there are: 2 * 336 * 720 = 483,840 line arrangements.

RELATED QUESTIONS
Suppose your family is having a reunion and all your grandparents, aunts, uncles and... (answered by ichudov)

How many arrangements are there for five people in a line for a photo if two of the five... (answered by edjones)

Seven people line up for a photo. How many different line ups are possible if 2 people... (answered by robertb)

You are lining up for a photo with 3 friends. How many different arrangements are... (answered by ikleyn)

A yearbook editor has selected 17 photos, including one of you and one of your friend, to (answered by stanbon)

A photographer is lining up 5 family members in a line for a picture. How many... (answered by Edwin McCravy)

30 people from 10 families of 3 attend a meeting. If 5 people are asked to sit on 5... (answered by Edwin McCravy)

A teacher has 7 students. They pose for a picture by standing in a single line. If the... (answered by jim_thompson5910)

A teacher has 6 students. They pose for a picture by standing in a single line. If... (answered by DrBeeee)