Combinations

[wabafet]

Hello. This is the problem: i have 3 apples, 4 pears and 3 plums and I have to deliver it to the 10 kids, so that one kid could recieve even one product. I thoutght, that it could be solved with combinations.
C10,3 * C7,5 * C3,3 aid it's 5040
Is that correct?

 

[soroban]

Hello, wabafet!

Your set-up is incorrect . . . and your arithmetic.

I have 3 apples, 4 pears and 3 plums.
I have to deliver then to 10 kids, so that each kid recieves one product.

I thought, that it could be solved with combinations.
. . \(\displaystyle C(10,3)\cdot C(7,{\bf5})\cdot C(3,3) \:=\:5040\)
. . . . . . . . . . . . . . ? . . . . . . . . . . . . . ?
Is that correct?

Choose 3 kids from the 10 kids and give them the 3 apples:
.. \(\displaystyle C(10,3) = 120\) ways.

Choose 4 kids from the remaining 7 kids and give them the 4 pears:
. . \(\displaystyle C(7,4)\,=\,35\) ways.

Choose 3 kids from the remaining 3 kids and give them the 3 plums.
. . \(\displaystyle C(3,3) \,=\,1\) way.

Therefore, there are:.\(\displaystyle 120\cdot35\cdot1 \:=\:4200\) ways.

 

[wabafet]

Ahh right, I made a mistake while I was writing. But, I figure out something, it could be permutations, because it doesn't matter which fruit child will receive, only thing that's important is that every kid receive even one.