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How many different subsets of the set {0, 1, 2, 3, 4, 5} do

$
0
0
(Source GMAT Club test)

How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

a) 16
b) 27
c) 31
d) 32
e) 64


The official answer is 32, but I did my math and arrived at 31. Would be of great help if someone could post their method. Thanks!

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