data management

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For MAMMALS, find the munber of:
a) 7-letter words
b) 7-letter word beggining with MA
c) 4-letter words
i) all letters different
ii) 2 letters same,2 different
iii) 2 pairs same letters
iv) 3 letters same

  • data management -

    I am not doing the problem for you but perhaps I can give you an idea.
    Let's see. I have to work with
    M M M A A L S
    If all letters were different the answer would be 7!, but they are not.

    Let me try a simpler example
    Say
    A A B B
    A B A B
    A B B A
    B A A B
    B B A A
    B A B A Hmm six of them, not 4!
    Looks like permutations of 4 items divided by permutations of 2 As divided by permutations of 2 Bs
    4!/(2!*2!) = 4*3*2 /( 2*2) = 6
    Let's try it with 3 As and 1 B
    A A A B
    A A B A
    A B A A
    B A A A Is that 4!/(3!*1!) ?
    4*3*2 /(3*2*1) = 4, sure enough.

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