Question: Arranging Buttons

Comment on Arranging Buttons

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.).

Any advice you can provide?

Thanks!
gmat-admin's picture

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 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?

gmat-admin's picture

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

Answer = (15)(6)(1) = 90

Does that help?

Cheers,
Brent

Fantastic explanation! Thanks Brent!!

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.

Thank you as always for your advice/help.
gmat-admin's picture

Great question!

The equation for the MISSISSIPPI Rule is not the same as the same as the Permutation formula.

Keep in mind that the MISSISSIPPI Rule handles situations in which we have some IDENTICAL objects that need to be arranged, whereas the Permutation formula handles situations in which the arranged objects are UNIQUE.

Cheers,
Brent

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