# Identical Green & Red Shirts

Discussion in 'Algebra' started by nycmathguy, May 19, 2022.

1. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
422
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

I sense this to be a probability question in disguise.

Is the set up like this?

Using Crn to represent the combination formula.

6C3 • 6C3

You say?

nycmathguy, May 19, 2022

2. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
6!/ ((3!) (3!)) = 20 ways that each child receives a shirt

MathLover1, May 19, 2022
nycmathguy likes this.

3. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
422
How did you come to that conclusion? How did you know what to do based on the wording given?

nycmathguy, May 19, 2022
4. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
it's just combination problem
C(6,3) -> choose 3 out of 6

MathLover1, May 20, 2022
nycmathguy likes this.

Joined:
Jun 27, 2021
Messages:
5,386