math 12

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A man bought two vanilla ice cream cones, three chocolate cones, four strawberry cones and one pistachio cone for his ten children. In how many ways can he distribute the flavors among the children?

  • math 12 -

    VVCCCSSSSP

    Well, the P can go 10 ways
    The V can go then 9*8 ways
    the C can go then 7*6*5
    and the S can go 4*3*2*1

    so ways: 10!
    check my thinking.

    but what if we did the strawberry first?

    the S can go 10*9*8*7 ways
    the V can go 6*5
    the P can go 4 ways
    the C can go 3*2*1
    again, 10!

    Believe me?

  • math 12 -

    Yes I did 10!/3!4!2!

  • math 12 -

    number of ways of n! of which we have a of one kind, b of another kind , c of another kind ...

    = n!/(a!b!c!..)

    so you would have 10!/(2!3!4!) = 12600

  • math 12 -

    that's what I got:) Thanks

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