Question 205844: 21. find the number of subsets of the set
{math,english,history,science,art}
a.28
b.32
c.16
d.24
Answer by dyakobovitch(40)   (Show Source):
You can put this solution on YOUR website! We have five subjects and we are dealing with combinations, not permutations here. We know that if we have five as a subset, there is 1 combination. 5C5. 4 as a subset, leaves us with 5 combinations... 5C4.
Notice how we are working with combinations in the problem. We want sets of 5, 4, 3, 2, 1, and 0 (or empty set).
With combinations, we need only add 5C5 + 5C4 + 5C3 + 5C2 + 5C1 + 5C0.
You can solve a combination based off the definition, which states that nCr= n!/(n-r)!, where ! denotes factorial.
So, 5C5 + 5C4 + 5C3 + 5C2 + 5C1 + 5C0 = 1 + 5 + 10 + 10 + 5 + 1 = 32. Your answer is "B".
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