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## Comment on

Distributing Coins## Can we solve this sum through

## As I mention in the video,

As I mention in the video, this question is out of scope for the GMAT. I wanted to use it to demonstrate the utility of listing and counting possible outcomes.

A "mathematical" approach would involve a technique known as "partitioning."

## I thought that we need to

## If you check the list, you'll

If you check the list, you'll see that {6,0,0}, {0,6,0} and {0,0,6} are already listed separately in the list of 28 outcomes.

## Hello, Didn't understand why

## To see what we can't use the

To see why we can't use the FCP, let's see what happens when we start.

STAGE 1: Give Alex some coins

We can give Alex 0, 1, 2, 3, 4, 5 or 6 of the coins.

So, we can complete stage 1 in 7 ways

STAGE 2: Give Bea some coins

In how many ways can we complete stage 2?

It depends on how many of the 6 coins we gave to Alex.

- If we gave 0 coins to Alex, then there are 6 coins remaining, which means we can give Bea 0, 1, 2, 3, 4, 5, or 6 coins.

- If we gave 1 coin to Alex, then there are 5 coins remaining, which means we can give Bea 0, 1, 2, 3, 4, or 5 coins.

- If we gave 2 coins to Alex, then there are 4 coins remaining, which means we can give Bea 0, 1, 2, 3 or 4 coins.

- If we gave 3 coins to Alex, then there are 3 coins remaining, which means we can give Bea 0, 1, 2 or 3 coins.

Etc...

So, there's no way to determine the number of ways to complete stage 2. The same goes for stage 3.

So, we need a different approach.

## Thanks, understood.

## Thank you! I had the same

## Hi Brent

Can we solve this question using fundamental counting principle?

Regards

Neha

## To my knowledge, there's no

To my knowledge, there's no nice way to solve this question using the Fundamental Counting Principle.

There is a technique, called the Separator Method, that we can use, but it's beyond the scope of the GMAT.

Cheers,

Brent

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