1. 11.3 Notes
Combinations

2. Warm-up (Permutations)
Consider the letters A, B, C, and D. What is the number of permutations of these four letters taken three at a time?
All Permutations:
ABC ABD ACD BCD
ACB ADB ADC BDC
BAC BAD CAD CBD
BCA BDA CDA CDB
CAB DAB DAC DBC
CBA DBA DCA DCB

3. Distinguishing Between Permutations and Combinations
A permutation is an ordered arrangement of a given group of items. With permutations order matters.
A combination is a group of items taken without regard to their order. With a combination, order does not matter.
Decide if the following is a problem involving permutations or combinations.
How many ways can you select 6 free DVD’s from a list of 200 DVD’s?
In a race in which there are 50 runners and no ties, in how many ways can the first three finishers come in?

4. Formula for Combinations
This formula indicates that there are r! times as many permutations for n things taken r at a time than there are combinations.
Example:
A three-person committee is needed to study ways of improving public transportation. How many committees could be formed from the eight people of the board of supervisors?

5. You try!
You volunteer to pet-sit for your friend who has seven different animals. How many different pet combinations are possible if you take three of the seven pets?
In poker, a person is dealt 5 card s from a standard 52-card deck. The order which the 5 cards are received does not matter. How many different 5-card poker hands are possible?

6. Combinations and the Fundamental Counting Principle.
In December 2009, the U.S. Senate consisted of 60 Democrats and 40 Republicans. How many distinct five-person committees can be formed if each committee must have 3 Democrats and 2 Republicans?

7. 11.3 MathXL
Due Sunday at midnight.