Combinations question

GMATprofessional21 wrote: ↑

Wed Aug 05, 2020 7:02 am

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 3 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

GMATprofessional21 wrote: ↑

Wed Aug 05, 2020 7:02 am

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

Solution:

The number of ways to distribute the shirts to the children is given by the number of arrangements of:

G - G - G - R - R - R

Since we have 6 total letters and 3 repeated G’s and 3 repeated R’s, we can arrange the letters in the following number of ways, using the indistinguishable permutations formula:

6! / (3! x 3!) = (6 x 5 x 4) / (3 x 2) = 5 x 4 = 20.

Answer: A