Results 1 to 3 of 3

Math Help - Probability Question

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    3

    Probability Question

    There are 6 letters, A-F. The GRE booklet problem involves arranging them in groups of 3. I already know the formula for this: n! divided by (n)(n-1). You get 20. But the question in my book asks how many of the groups of 3 contain the letter F. How does one figure that out with a formula instead of writing them all out? Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Combinatorics

    Hello GREhelp
    Quote Originally Posted by GREhelp View Post
    There are 6 letters, A-F. The GRE booklet problem involves arranging them in groups of 3. I already know the formula for this: n! divided by (n)(n-1). You get 20. But the question in my book asks how many of the groups of 3 contain the letter F. How does one figure that out with a formula instead of writing them all out? Thanks in advance.
    I'm not quite sure where you arrive at \frac{n!}{n(n-1)}. This gives (n-2)!, which is 24 if n = 6.

    (a) How many groups of 3 can we choose from 6 items? Answer: \binom{6}{3}=\frac{6!}{3!3!}= 20.

    (b) How many groups of 3 contain the letter F? Answer: the same as the number of ways of choosing the other 2 letters from 5, which is \binom{5}{2}= \frac{5!}{2!3!}= 10.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    3

    Thanks for the answer!

    Thanks Grandad for cleaning up my initial equation -- yeah, I had meant: n! divided by (n-r)!(r!) to get the total # of combinations. So to get the number of F's, you have to find out how many ways the other letters will combine with it in groups of 2 (from 5). Thanks for the solution formula!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: February 10th 2013, 02:11 PM
  2. Probability question involving (A given B type question )
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 9th 2009, 09:08 AM
  3. Probability Question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 2nd 2009, 06:57 AM
  4. Probability Question
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: November 25th 2007, 08:16 PM
  5. A probability question and an Expectations question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 29th 2006, 06:13 PM

Search Tags


/mathhelpforum @mathhelpforum