math 12
posted by kitkat on .
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?

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

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 
that's what I got:) Thanks