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Using the following bills $1, $5, $10, $20, $50, how many

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Director
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Using the following bills $1, $5, $10, $20, $50, how many [#permalink] New post 22 Jan 2005, 21:05
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Using the following bills $1, $5, $10, $20, $50, how many unique sums can be formed using each bill only once?

a) 20
b) 24
c) 31
d) 74
e) 120
SVP
SVP
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 [#permalink] New post 22 Jan 2005, 21:19
You could choose 1 bill from the five given bills, each one obviously give you different sums. (1C5)
Then you could also choose 2 bills from the five given bills, this will give you different sums from each other and from what you have in step one. (2C5)
Then you could choose 3 bills from the five ...
So on and so forth
Until you choose all of them adding together, that is another different sum from the previous one. (5C5)

So total possible ways is 1C5+2C5+3C5+4C5+5C5=2(1C5+2C5)+1=2(5+5*4/2)+1=31
Director
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 [#permalink] New post 23 Jan 2005, 16:33
I don't get this one. PLease explain further
VP
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 [#permalink] New post 23 Jan 2005, 19:28
As there r no duplicate bills....we can use combinations of 1,2,3,4,5 bills to get unique sums

1 bill = 5
2 bills = 5C2 = 10
3 bills = 5C3 = 10
4 bills = 5C4 = 5
5 bills = 1

Total = 31 sums
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 [#permalink] New post 23 Jan 2005, 23:10
I suppose my denotion of combination was what is confusing. :blush: I guess I should have used 5C1 etc. instead of 1C5.
  [#permalink] 23 Jan 2005, 23:10
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Using the following bills $1, $5, $10, $20, $50, how many

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