for example you have a 5 pound coin a 2 pound coin and a 1 pound coin. you need to make 8 pound what are the seven different ways you can make 8 pounds
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1+1+1+1+1+1+1+1=8 (Eight 1's) , 2+1+1+1+1+1+1=8, (Six 1's, One 2), 2+2+1+1+1+1=8 (Four 1's, Two 2's), 2+2+2+1+1=8 (Two 1's, Three 2's), 2+2+2+2=8 (Four 2's), 5+1+1+1=8 (Three 1's, One 5), 5+2+1 (One 1, One 2, One 5)
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the possible combinations are
5+2+1
5+1+1+1
2+2+2+2
2+2+2+1+1
2+2+1+1+1+1
2+1+1+1+1+1+1
1+1+1+1+1+1+1+1
5+2+1
5+1+1+1
2+2+2+2
2+2+2+1+1
2+2+1+1+1+1
2+1+1+1+1+1+1
1+1+1+1+1+1+1+1