# 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.

### Hi Brent, not sure why is not

Hi Brent, not sure why is not multiplication of each outcome but addition for total combinations here? Is this because it's not based on FCP? Getting a bit confsued. Thanks ### For this question, we are

For this question, we are simply listing and counting all of the possible outcomes.
So there's no need to introduce any other operations.

You are correct about the FCP. Since we are not using the FCP to answer the question, there's no need to multiply.

### Get it, thanks Brent

Get it, thanks Brent