How to watch avengers

6 friends went to the cinema to watch a new movie. Then they realized that 2 of them are a couple and cannot be separated. How many different ways they can sit in the movie theatre?


The answer is 240.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Zico Quintina
May 2, 2018

To keep the couple together, we temporarily treat them as one person. Then we are arranging five "people", which can be done in 5 ! 5! ways. Once that's done, the couple itself can switch seats among themselves, which can be done in 2 ! 2! ways. So the number of ways the six can sit keeping the couple together is 5 ! 2 ! = 240 5! \cdot 2! = \boxed{240}

The couple must be placed together and we can ignore them for the moment. The remaining 4 friends can be placed in the other 4 seats in 24 ways - there are 4 different people who can go in the first seat, 3 in the second, 2 in the third and 1 in the fourth, multiply 4 by 3 by 2 by 1 and you get 24. The couple can be placed in 5 ways: seat 1 and 2, seat 2 and 3, seat 4 and 5, seat 5 and 6. However, the two people in the couple can be swapped around doubling the numbers of possible combinations for the couple to 10. 24 multiplied by 10 is 240.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...