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?

10 comments:

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

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

    ReplyDelete
  3. 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.

    www.guessthelogo.blogspot.com

    ReplyDelete
  4. 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%.

    ReplyDelete
  5. 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.

    ReplyDelete
  6. 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?

    ReplyDelete
  7. 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.

    ReplyDelete

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