06/19/2020 (2011: Countdown Round, Problem 17)

Q: How many subsets of a nine-element set have an odd number of elements?

A: 256

There are 9C1 = 9 ways to choose a one-element subset.

There are 9C3 = 84 ways to choose a three-element subset.

There are 9C5 = 126 ways to choose a five-element subset.

There are 9C7 = 36 ways to choose a seven-element subset.

There are 9C9 = 1 way to choose a nine-element subset.

9 + 84 + 126 + 36 + 1 = 256