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

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.