1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Probability problem (#of ways to seat a couple) *edit: solved*

  1. Mar 25, 2013 #1
    *edit: solved! I counted everything twice.

    1. The problem statement, all variables and given/known data

    How many ways are there to seat 10 people, consisting of 5 couples, in a row
    of seats (10 seats wide) if all couples are to get adjacent seats?

    3. The attempt at a solution
    I'm trying to look calculate it at a couple level.

    10 seats available, 5 couples
    _ _ _ _ _ _ _ _ _ _

    first couple has 9 choices to choose from They can't choose seat # 10 or else they will not sit next to each other. they can also swap seats, so that will be 9 x 2 = 18 choices.

    second couple will have 7 seats to choose from. They can trade seats, so that will be 7 x 2 = 14

    third couple has 5 seats, trade seats an yield 10.

    fourth couple has 3 seats, = 6

    5th couple has 2 seats left, they can trade once, so that is 2 possibilities

    I did 18 x 14 x 10 x 6 x 2 = 30,240. answer key says 3840 though?
    Last edited: Mar 25, 2013
  2. jcsd
  3. Mar 25, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Since you have already found the correct answer, I will share another way to get there.
    As each couple has to sit next to each other, you basically have 5 two-seat blocks to distribute the 5 couples over. The number of ways in which this can be done is just 5! because every permutation of the couples will give a different assignment of couples to two-seat blocks. Then within each block you can swap the two persons, so you get [itex]5! \cdot 2^5[/itex] possible ways.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted