In how many different ways can 3 identical green shirts and

BTGmoderatorDC wrote: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?

A. 20
B. 40
C. 216
D. 720
E. 729

OA A

Source: Magoosh

If there are p numbers of identical items, q numbers of identical items, and r numbers of identical items, the total number of way, (p + q + r) items be distributed is given by (p + q + r)! / (p!*q!*r!).

Thus, the number of ways 3 identical green shirts and 3 identical red shirts be distributed among 6 children = 6! / 3!*3! = 20

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorDC wrote: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?

A. 20
B. 40
C. 216
D. 720
E. 729

We can take this question and ask an easier question: In how many ways can we choose 3 of the 6 children to receive a green shirt?

Notice that, once we have given a green shirt to each of those 3 chosen children, the remaining children must get red shirts. In other words, once we have given green shirts to 3 children, the children who get red shirts is locked.

So, in how many ways can we select 3 of the 6 children to receive a green shirt?
Since the order of the selected children does not matter, this is a combination question.
We can choose 3 children from 6 children in 6C3 ways (= 20 ways)

Answer: A

Cheers,
Brent