1. Combinations

2. Definition of Combination
An arrangement of objects in which the order of selection does NOT matter.
Ex: You have to visit three out of your four friends houses: Andrew (A), Betty (B), Carlos (C), Dave (D). What are the different ways to select the 3 houses to visit?
A,B,C
A,C,D
A,B,D
B,C,D
Each arrangement is one combination of the elements A, B, C, and D. In other words, there are 4 total combinations.

3. Combination Example NO!
A bag has 7 marbles (blue, green, red, yellow, orange, purple, and black). If you select four marbles at once, how many combinations are possible?
a. How many ways can you arrange 4 marbles from 7?
NO!
b. Is selecting BGRY different than BRGY?
c. How many ways can you arrange B, G, R, and Y?
d. How many combinations are possible?

4. Combination
The total number of ways (without repeats) to choose r objects from a set of n objects (order does NOT matter).
Ex: Jim had 9 friends and needs to select 4 of them to go on a trip. How many different arrangements are possible?