Posted by **Bryan** on Thursday, January 26, 2012 at 7:57pm.

Assume that the set S has 7 elements.

How many subsets of S have at most 3 elements

- Finite MAth -
**Reiny**, Thursday, January 26, 2012 at 8:26pm
The total number of subsets = 2^7 = 128

This includes the null set

So what we want is

the null set, the set of singles, the set of doubles and the set of triples

= 1 + C(7,1) + C(7,2) + c(7,3)

= 1 + 7 + 21 + 35

= 64

So the number of subsets with at most 3 elements is 64

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