Question 778981: You have a handful of quarters, nickels, and dimes that totals 75 cents. Make a table listing all possible combinations of coins. Answer by Edwin McCravy(20054) (Show Source):
I will assume that you necessarily have at least one of each
kind of coin. (For instance, 3 quarters is not allowed, nor
is 15 nickels, nor 7 dimes and 1 nickel.)
If you have 1 quarter, you can have from 1 up through 4 dimes,
and the rest in nickels. That's 4 ways.
If you have 2 quarters, you can have either 1 or 2 dimes and
the rest in nickels. That's 2 more ways.
So there are a total of 4+2 or 6 combinations of coins you
can possibly have:
Number of Number of Number of
Combination# Quarters dimes nickels
1 1 1 8
2 1 2 6
3 1 3 4
4 1 4 2
5 2 1 3
6 2 2 1
You might impress your teacher by showing her or him that
you can also make a TREE diagram for that problem,
like this: (See if you can figure it out)
Edwin