Question

Jayne has 3 quarters, 2 dimes, a nickel and 2 pennies in her pocket. How many different amounts of money can she make using some or all of her change?

Answer 1

Without trying to list all of them, I just now thought of a way to figure out the number of different possibilities:

The total can be made from:

-- zero, 1, 2, or 3 quarters . . . 4 choices
-- zero, 1, or 2 dimes . . . . . . . 3 choices
-- zero or 1 nickel . . . . . . . . . . 2 choices
and
-- zero, 1, or 2 pennies . . . . . . 3 choices

So there are (4 x 3 x 2 x 3) = 72 different possible combinations of coins

Almost all of the possible combinations appear to be unique. I do
see one possible duplication: 1qtr is the same thing as (2dim + 1nkl).
That reduces the number somewhat, but I don't really know how to handle it.

So the number of different amounts of change is a few less than 72 .


I hope this answer is worth 5 points.