Question 1096554: If you were to solve at least 1 but at most 5 problems from this set of 10 problems, how many problem subsets are there that may be solved?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
You need to choose either 1, 2, 3, 4, or 5 of the 10 problems. The numbers of ways to do that are "10 choose 1", "10 choose 2", ..., and "10 choose 5".
The easiest way to find those numbers is to look at the 5th row of Pascal's Triangle, which begins
1, 10, 45, 120, 210, 252, ...
Those numbers are 10 choose 0, 10 choose 1, ..., 10 choose 4, and 10 choose 5.
So the number of ways to choose at least 1 and at most 5 problems is
10+45+120+210+252 = 637
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