SOLUTION: how many amounts can you make from 1 dime 2 nickles and 3 pennies

Question 668539: how many amounts can you make from 1 dime 2 nickles and 3 pennies
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
By our fundamental counting principle, we can make 2 * 3 * 4 different combinations of dimes, nickles, and pennies (you may think 1*2*3, but remember there's actually one extra way for each coin and that is to have 0 coins).
So there are 24 different combinations. Now do any of these coins yield the same amount? Notice that 2 nickels = dime. Notice that there are eight cases where we have either a certain number of pennies (0-3) + dime or a certain number of pennies (0-3) + 2 nickels. So, we need to eliminate either the dime case or the 2 nickels case. Either way gives us 4 less ways. And so we can have 20 distinct amounts for our coins. If your teacher does not consider the all 0 case to be an amount, then there are really only 19.
These amounts being
(0)
1
2
3
5
6
7
8
10
11
12
13
15
16
17
18
20
21
22
23
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19 or 20 different amounts depending on 0 case
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