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Math Help - No. of possible 'words'

  1. #1
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    No. of possible 'words'

    In this question, a 'word' is defined to be any set of letters in a row, whether of not it makes sense. Find how many different 'words' can be made using only 5 letters of the word SYLLABUS

    I tried to separate them into 4 cases,

    1) all different letters
    2) 2 'S'
    3) 2 'L'
    4)2 'S' and 2 'L'
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  2. #2
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    Re: No. of possible 'words'

    Hello, Punch!

    In this question, a 'word' is defined to be any set of letters in a row,
    whether of not it makes sense. . Find how many different 'words'
    can be made using only 5 letters of the word SYLLABUS.

    I tried to separate them into 4 cases,

    1) all different letters
    2) two S's
    3) two L's
    4) two S's and two L's


    An excellent game plan! How far did you get?

    We have 8 letters, 6 distinct: . A,B,LL,SS,U,Y

    1) Five different letters
    . . Choose 5 of the 6 letters and permutate them:. _6P_5 \,=\,720

    2) Two S's: . S\,S\,\_\,\_\,\_
    . . Choose 3 of the other 5 letters:. _5C_3 \,=\,10
    . . and permute the 5 letters:. 10\cdot\tfrac{5!}{2!} \,=\,600

    3) Two L's:. L\,L\,\_\,\_\,\_
    . . Choose 3 of the other 5 letters:. _5C_3\,=\,10
    . . and permutate the 5 letters:. 10\cdot\tfrac{5!}{2!}\,=\,600

    4) Two S's, two L's:. S\,S\,L\,L\,\_
    . . Choose 1 of the other 4 letters:. _4C_1\,=\,4
    . . and permutate the 5 letters:. 4\cdot\tfrac{5!}{2!\,2!}\,=\,120


    There are:. 720 +600 + 600 +120 \:=\:2040 "words".

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