how many different sums can be made from penny, nickel, dime

[flyingfreedom]

Assuming that at least one coin is used, how many different sums of money can be made from the following coins: a penny, a nickel, a dime, a quarter , and a dollar?

I've found a way to solve these kind of problems 2^n-1, where n=amount of different coins. So the answer is 31. I did

2^5=32
32-1=31

But how are you supposed to solve these kind of questions, and what would happen if there were for instance two pennies, three dimes....
Thanks so much

 

[Deleted member 4993]

Re: word problem

Assuming that at least one coin is used, how many different sums of money can be made from the following coins: a penny, a nickel, a dime, a quarter , and a dollar?
I've found a way to solve these kind of problems 2^n-1, where n=amount of different coins. So the answer is 31.
I did 2^5=32
32-1=31
But how are you supposed to solve these kind of questions, and what would happen if there were for instance two pennies, three dimes....
Thanks so much

These are counting problems.

You use "combination" to solve these problems.

In this problem you cold choose 1,2,3,4 or 5 coins each time getting a different answer

How many ways you can choose 1 coin .............5

How many ways you can choose 2 coins ........[sub:3fiadtqa]5[/sub:3fiadtqa]C[sub:3fiadtqa]2[/sub:3fiadtqa] = 10

How many ways you can choose 3 coins ........[sub:3fiadtqa]5[/sub:3fiadtqa]C[sub:3fiadtqa]3[/sub:3fiadtqa] = 10

How many ways you can choose 4 coins ........[sub:3fiadtqa]5[/sub:3fiadtqa]C[sub:3fiadtqa]4[/sub:3fiadtqa] = 5

How many ways you can choose 5 coin .............1

All added up is 31

You can prove that in case you have 'n' different coins - the sum would be 2[sup:3fiadtqa]n[/sup:3fiadtqa] - 1

Now the explaining the case of duplicate coins become difficult in this forum format. You may want to do some google search or read up books on combinatrics (or counting principles). Another thing you may have to watch out for - when two different combinations give you the same amount of money - like 'two dimes and nickel' vs. 'one quarter'.