(Part 1)
ALL POSSIBLE COMBINATIONS of DISTINCT ITEMS
EXAMPLE #1 Barney’s refrigerator contains 1 apple, 1 orange, and 1 pear.
Determine the number of ways that he can select at least one piece of fruit for a snack.
METHOD 1: Using COMBINATIONS
METHOD 2: Using SUBSETS
Each subset is one combination of elements.
For a set of n elements, there are 2 n subsets including the null set.
The total number of combinations containing at least one item
chosen from a group of n distinct items is 2 n – 1.
EXAMPLE #2 Determine the number of ways a committee with at least 1 member can be appointed from a board with 6 members.

ALL POSSIBLE COMBINATIONS with SOME IDENTICAL ITEMS
EXAMPLE #3 A gym locker contains 6 volleyballs, 3 basketballs, 5 tennis balls, and 2 golf balls. Determine the number of ways Barney can select at least 1 sport ball for gym class.
( )( )( )( )
VB BB TB GB
In a situation where it is possible to choose all, some, or none of the n items available, there are (n+1) choices.
If at least one item is chosen, the total number of selections that
can be made from p items of one kind, q items of another kind,
r items of another kind, and so on is:
(p + 1)(q + 1)(r + 1) … – 1
EXAMPLE #4 A cookie jar contains 5 peanut butter, 6 chocolate chip, and 3
Oreo cookies. Determine the number of ways the cookie monster can select some cookies.
HOMEWORK: p.286-287 #1 – 5,6a, 7a, 13