Question: Distributing Coins

Comment on Distributing Coins

Can we solve this sum through some different methodology, given the method illustrated will not be feasible in exam?
gmat-admin's picture

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 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
gmat-admin's picture

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 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 :(
gmat-admin's picture

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 doubt.

Hi Brent
Can we solve this question using fundamental counting principle?

Regards
Neha
gmat-admin's picture

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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