# Question: Distributing Coins

## Comment on Distributing Coins

### Can we solve this sum through

Can we solve this sum through some different methodology, given the method illustrated will not be feasible in exam? ### 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

I thought that we need to consider 28 times 3 because the option (6,0,0) is different from (0,6,0) and from (0,0,6)... Where is my mistake? tks ### 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

Hello, Didn't understand why can't we use fundamental counting principle here? This is three stage activity and for each activity we need to distribute 0 to 6 coins. confused :( ### 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.

Thanks, understood.

### Thank you! I had the same

Thank you! I had the same doubt.

### Hi Brent

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

### in probability theory from my

in probability theory from my university I learned you can use n+r-1 choose r-1 to solve this problem. ### That's correct. However, the

That's correct. However, the GMAT does not require us to know this rule.