Question

In how many ways can I distribute $6$ identical cookies and $6$ identical candies to $4$ children, if each child must receive exactly $3$ items? (The requirement from part (a) is no longer in force -- that is, it's OK now to give a child $3$ items of one type and none of the other.)

Answer 1

You can distribute the cookies and candies in four ways.

Explanation:

Since cookies and candies are indistinguishable, we can use a combination. In this case represents the number of possible ways to distribute (without repetition) the cookies and candies (p) among a given number of children (n):

`\begin{pmatrix}n\\ p\end{pmatrix}=(n!)/(p!(n-p)!)\\\begin{pmatrix}4\\ 3\end{pmatrix}=(4!)/(3!(4-3)!)=(4!)/(3!1!)=4`