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
To solve this problem, we need to use the combination formula. We have 6 children and we need to choose 3 of them to receive the green shirts. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes a factorial.
Substituting into the formula gives:
C(6, 3) = 6! / [3!(6-3)!] = (654) / (321) = 20
So there are 20 different ways to distribute the shirts among the children.
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