Arrangements of ABCDEF

GRE Quant Problem Solving
1 
A, B, C, D, E and F are six friends attending a movie together. A and B
want to sit together, C and D want to sit together, and E and F want to
sit together. Unfortunately, the usher randomly assigns the six friends
together in a row. What is the probability that all six friends sit next to
whom they want?

Hi Team,
I attempted this question with the following equation.

1/6* 5/5* 1/4* 3/3* 1/2* 1/1 =1/48

Can someone highlight why it didn’t work?

2

Can B and A sit together?

3

Yes.

4

Let’s look at it this way. You have three groups of people

[A, B], [C, D], [E, F]

There are two things to consider:

  • how many ways you can interchange within the groups
  • how many ways you can swap the groups themselves.
5
  • how many ways you can interchange within the groups= 2!
  • how many ways you can swap the groups themselves = 3!
6

Correct. Notice though that given that we can interchange any one group in 2 ways, we can interchange any of the three groups in 2^3 = 8 ways.

Can you use that to get the final answer?

Also: Greg has a video solution for that one - have you seen it? It’s closer to what you’ve done.