Math Is Fun Forum

Tony Wong

Guest

Combinatorics

"Jayne has 3 quarters, 2 dimes, a nickel, and 2 pennies in her pocket. How many different amounts can she make using some or all of these coins?" Please solve this and show me how you got the answer step-by-step.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Combinatorics

Please solve this and show me how you got the answer step-by-step.

This sounds as if you’re asking us to do your homework for you. Sorry, but homework is somethng you have to do yourself.

However we can guide you on how to do your homework. One way to do the problem is to make a table showing all possible combinations of coins and what they amount to.

You can do this table easily with an Excel spreadsheet. You should get 71 combinations of the Q, D, N, P – but note that not every combination produces a unique amount (e.g. 1Q+2D+1N+2P = 2Q+0D+0N+2P).

Last edited by JaneFairfax (2007-09-28 13:38:10)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Combinatorics

An alternate method is to try to find the amounts she can't make.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Combinatorics

And also this problem has nothing to do with probability. Shouldn’t the title be changed to something more relevant to the subject?

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Combinatorics

And also this problem has nothing to do with probability. Shouldn’t the title be changed to something more relevant to the subject?

In my country, this kind of question falls under probability lesson.

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bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combinatorics

"Jayne has 3 quarters, 2 dimes, a nickel, and 2 pennies in her pocket. How many different amounts can she make using some or all of these coins?" Please solve this and show me how you got the answer step-by-step.

Use generating functions:

But we need to use some of the coins so 0 is out. There are 71 ways to give change using these coins but only 62 of them are different amounts so that is the answer.

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In mathematics, you don't understand things. You just get used to them.
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