I have three $50 bills, ten $20 bills and five $10 bills in my wallet. How many different ways are there for me to pay an invoice of $200 using exactly ten bills?
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There are three possible combinations to sum up $200 using ten bills. To understand the combinations easier, $ sign will be omitted.
2 0 0 = ( 2 0 ∗ 1 0 )
2 0 0 = ( 5 0 ∗ 1 ) + ( 2 0 ∗ 6 ) + ( 1 0 ∗ 3 )
2 0 0 = ( 5 0 ∗ 2 ) + ( 2 0 ∗ 2 ) + ( 1 0 ∗ 6 )
As I have only five $10 bills, the third method should be omitted. Therefore the answer is 2.