How to find the # of subsets in a set?
Theorem
No Identical Items
Remember that combinations are subsets of the group of n objects, a null set is a set that has no elements, thus:
A set with n distinct elements has 2^n subsets including the null set.
Thus:
Total number of combinations containing at least one item chosen from a group of distinct items is 2^n - 1.
Used nicely in Problem Solving with Combinations
Example Problems
The director has 5 rock songs, 2 blue songs and 3 jazz pieces. how many ways can the director choose 3 pieces of sound track, if film wants to include some jazz?
All songs = 5+2+3 = 10 All combinations = _1$$_0C …