# Data Management

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How many different sums of money can be formed from one \$2 bill, three \$5 bills, two \$10 bills, and one \$20 bill?

the answer at the back of the book is 23, but i don't know how to solve it.

• Data Management -

We note that the question requires different sums of money, irrespective of how they are made up, it is important not to double count. For example 1-\$10 and 2-\$5 bills should be counted as one sum.

Start with the multiples, namely the \$5, \$10, and \$20 bills. The possible sums range from \$0 to \$55 in \$5 increments. That makes 12 possible sums.

By adding a \$2 bill, we get 12 more sums, namely from \$7 to \$57 in \$5 increments. This makes a total of 24 sums, including \$0.

If the question implies at least one bill must be used, then there are 23 sums.

• Data Management -

is there a formula for this?

• Data Management -

Yes, I believe there is one called the combination formula, search it up.

And yes, I do realise I'm replying to a comment from 2010. Hope it was worth the wait. :)

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