## Tuesday, September 01, 2009

### Going to the Theatre

Two men and two women went to the movie theater together and they all sat in the same row.  The two men want to be in the middle so that there are two women at either end, but don't want to force anything.  What are the chances that things will work out for them?

1. I got 1/6 chance but I'm not sure it's right.

2. 25%

3. Are they gay also?
lol

4. I got 1/6 too (4 arrangements/24 possible).

5. There could be 2 answers, depending on how you interpret the question.

Scenario 1 : Man and woman pair are always together than the answer 1/8.
Scenario 2: Man and woman pair does not necessarily sit together then the answer is 1/6.

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6. 4/24 = 1/6

7. Alright, I'm a bit confused by the answers given. I'm thinking I must have worded the problem incorrectly.

There are only 10 possible arrangements. You can either write them out, or you can use 5 choose 2 formula. Here's the listing:
WWWMM
WWMWM
WMWWM
MWWWM
WWMMW
WMWMW
MWWMW
WMMWW
MWMWW
MMWWW

Of those, only three have two women on both ends. So the probability is 30%.

8. Mike, um, there are only two couples = 4 people. Without differentiating between the 2 men or the 2 women, there are 6 possible arrangements and only one has the 2 women in the middle.

9. With two men and two women:

1. W W M M
2. W M W M
3. W M M W
4. M W W M
5. M W M W
6. M M W W

Is this what Anonymous was saying? 1 in 6?

10. I knew there was something wrong. Sorry about that. It was supposed to be three women. Thanks for figuring this out for me.

This is one of those cases where I was seeing what I was thinking, not what was written.

The answer for the question as it is written is 1/6 as USAF Pilot and anonymous point out.

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