Question

A set has 9 elements. How many subsets have at most 3 elements?

Answer 1

The empty set,
a set that contains only one term.. so 10 so far..

Answer 2

and then a set that contains 2 terms, so 8 more, 18 so far

Answer 3

C(9,3)+C(9,2)+C(9,1)+1(for the empty set)?

Answer 4

yea basically

Answer 5

The total number of ways we can pick a subset of a set, with a subset length \(|P|\) and a set length of \(|S|\) is:
\[
\binom{|S|}{|P|}
\]So, we get:
\[
\binom{9}{0}+\binom{9}{1}+\binom{9}{2}+\binom{9}{3}
\]

Answer 6

Thanks!