# Question: Arranging Buttons

## Comment on Arranging Buttons

### Hey Brent,

Hey Brent,

Why would this not be a combination question? I understand the ordering fundamental, but I tend to get confused on questions like these because it seems that ordering does not matter (you could have RBG, BRG, etc.).

Thanks!

### If you can show me how you

If you can show me how you might set this up as a combinations question, then I might be able to identify the issue.

In the meantime, this video examines the issue of when to use combinations: https://www.gmatprepnow.com/module/gmat-counting/video/788

Cheers,
Brent

### Can we solve the question

Can we solve the question this way...

Buttons,

R1, R2 can be arranged in 6 * 5 ways
B1, B2 cab be arranged in 6 * 5 ways and
G1, G2 can be arranged in 6 * 5 ways.

So the 6 buttons can be arranged in 30 + 30 + 30 = 90 different ways?

### Although you do arrive at the

Although you do arrive at the correct answer (90), this is just a coincidence.

First of all, the two red buttons can be arranged in 15 ways (not 30 ways).
We have 6 spaces where the buttons can be placed: 1st, 2nd, 3rd,...6th
We must select 2 spaces
Since the order in which we select the spaces does not matter, we can use combinations.
We can select 2 spaces from 6 spaces in 6C2 ways (15 ways)

Once we've placed the 2 red buttons, we can now place the 2 blue buttons.
There are now 4 spaces remaining.
We must select 2 spaces for the blue buttons.
Since the order in which we select the spaces does not matter, we can use combinations.
We can select 2 spaces from 4 spaces in 4C2 ways (6 ways)

Once we've placed 4 red buttons, there are now 2 spaces remaining.
So, the green buttons must be placed in those 2 remaining spaces.
So, we can complete this stage in 1 way

Does that help?

Cheers,
Brent

### Fantastic explanation! Thanks

Fantastic explanation! Thanks Brent!!

### Hey Brent, just wanted to

Hey Brent, just wanted to clarify something.

does the MISSISSIPPI rule follow the same equation as the Permutation Formula?

Such that cPr=n!/(n-r)!

You advise in earlier videos that you do not teach the Permutation formula given that most GMAT counting question can be solved via FCP. However, when I see the MISSISSIPPI rule, I instantly tie it to "Arrange/Permutation" questions - which most people on GMAT forums solve via the Permutation formula.