In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt
Question
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt
Solution
Since the shirts are identical within their color groups, we only need to consider how to distribute the colors among the children, not the individual shirts.
This is a combination problem. We have 6 children and we need to choose 3 of them to receive the green shirts. The other 3 will automatically receive the red shirts.
The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where: n is the total number of items, k is the number of items to select, "!" denotes factorial, which is the product of all positive integers up to that number.
Substituting the given values into the formula, we get:
C(6, 3) = 6! / [3!(6-3)!]
= 6! / [3! * 3!]
= (6 * 5 * 4) / (3 * 2 * 1)
= 20
So, there are 20 different ways to distribute the shirts among the children.
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