1. Not finding help here? Sign up for a free 30min 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!

Disc. math: permutations

  1. Apr 14, 2010 #1
    How many permutations of the letters ABCDEFGH contain the string ABC?

    This is an example problem in my book, and the answer is 6! = 720. Could someone please explain to me the reasoning behind this (my book does a poor job explaining)? And would this reasoning apply if the string to be found was, say, just AB?
     
  2. jcsd
  3. Apr 15, 2010 #2

    Filip Larsen

    User Avatar
    Gold Member

    Since ABC has appear just like that you can treat ABC as an indivisible block just like the other letters so that you have ABC, D, E, F, G and H, i.e. 6 blocks in all to find permutations for, which is 6! = 720.
     
  4. Apr 15, 2010 #3
    OK, I see now. Thank you. Here's another problem I'm stuck on:

    A department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have more women than men?

    What I figure out so far is that this would be a combination, not a permutation. If gender was not a concern, it could just simply be C(25, 6). Since there must be MORE women than men, there are gender possibilities: WWWWWW, WWWWWM, WWWWMM. At first glance, it looks like you might be able to just half the amount of answers, but the amount of women and men are not equal. I tried an approach like this:

    C(10, 2) + C(10, 1) + C(13, 4) + C(13, 5) + C(13, 6)

    but I'm not sure if this is correct.


    *C(n, r) = n!/(r!*(n-r)!)
    this is the combination theorem for number of r-combinations of a set with n elements.
     
  5. Apr 15, 2010 #4

    Mark44

    Staff: Mentor

    Given the restrictions, the committee must fall into one of three types:
    4 women, 2 men
    5 women, 1 man
    6 women.
    Find the number of combinations for each of the three committee arrangements and add them.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Disc. math: permutations
Loading...