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Possibilities Question.

  1. Jan 17, 2006 #1
    Question: How many four letter words can be made in increasing order. For instance, "aade" is a possibility, but "adae" is not.

    Solution: I honestly don't understand how I can solve this, I tried making a formula but it doesn't seem to work. The formula I came up with is: 1 + (3 x (25-n)) where n = 0 when the alphabet is a, n = 1 when the alphabet is b, and so forth. Any help would be greatly appreciated since I have to hand in the solution to this problem by tomorrow morning's class.

    :surprised

    Thanks.
     
  2. jcsd
  3. Jan 18, 2006 #2

    arildno

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    Your first letter can be any one between 1 and 25; call it k.
    We have 1<=k<=25
    Your second letter can be any one between k and 25, call it l
    We have k<=l<=25
    Your third letter can be any one between l and 25, call it m.
    We have l<=m<=25
    Your fourth letter can be any one between m and 25; call it n
    We have m<=n<=25.

    Thus, counting up all possibilities we've got (call that number P), we may write:
    [tex]P=\sum_{k=1}^{25}\sum_{l=k}^{25}\sum_{m=l}^{25}\sum_{n=m}^{25}1[/tex]

    What remains is to perform the summation. :smile:
     
    Last edited: Jan 18, 2006
  4. Jan 18, 2006 #3

    Galileo

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    Do you need to use the 4 letters a,a,d,e? With the 'a' twice?
    In that case, simple counting will do.

    Anyhoo, you might as well use numbers instead of letters a,b,c <-> 1,2,3,....
    Maybe that's easier to use.
     
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