Question: Distributing Coins

Comment on Distributing Coins

why isn't here "multiply"? can you explain it please?
greenlight-admin's picture

In this lesson, we're looking at the technique of Listing & Counting, in which we simply list all possible outcomes and them count those outcomes.

So, there aren't any sophisticated counting techniques involved here (like using the Fundamental Counting Principle, which involves multiplication)

can you please explain how can we solve same question, using fundamental counting principle?

greenlight-admin's picture

There's no way to solve this question using the fundamental counting principle, unless we consider a crazy number of cases. The purpose of the question is to show the utility of listing and counting.

I have one more question,

how many 3 digit number can be formed so that addition of 3 digit will yield 6. choose any digit out of 0,1,2,3,4,5,6.

please help me in understanding this.
greenlight-admin's picture

That question requires us to use a technique known as partitioning, which is beyond the scope of the GRE.

If you're interested in learning more, see my response to the the following question:

Thanks for saying that this would never be on the GRE. It's true.

Why is (0, 0, 6) not a possibility? Or even (0, 6, 0)?
greenlight-admin's picture

Those outcomes are in the solution. See 2:10 in video.

Hey Admin, as the coins are identical that why we are using counting and not some combination technique as if they were different wouldnt we muliply 28( The Answer) with 2 to account for B and C
greenlight-admin's picture

The solution method (listing and counting) takes into account the fact that the coins are identical.

For example, the distribution {5, 1, 0} (where Alex receives 1 coin, Bea receives 1 coin, and Chad receives 0 coins), is counted as exactly ONE outcome.
If the 6 coins were not identical (let's call them coins A, B, C, D, E and F), then we would get 6 different outcomes for {5, 1, 0}, since Bea could receive coin A (and Alex would receive the remaining 5 coins), OR Bea could receive coin B (and Alex would receive the remaining 5 coins), OR Bea could receive coin C (and Alex would receive the remaining 5 coins), etc.

We COULD use a technique called partitioning to solve the original question, but I believe this technique is beyond the scope of the GRE, since I've never seen an official question that would require it.

The main purpose of this video is to show that there are times when listing and counting prove to be a useful strategy. So, don't worry if you were unable to solve it using conventional counting techniques.

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