Lesson 8.6 Page 634-636 #1-21 (ODD), 23-31 (EOO), 33-45 (ODD), 47-55 (EOO), 57-69 (ODD) Pick up the handout on the table
Jan 13, 2016
Lesson 8.6
Page 634-636
#1-21 (ODD), 23-31 (EOO), 33-45 (ODD), 47-55 (EOO), 57-69 (ODD)
Pick up the handout on the table
Counting Principles
Objective
Students will know how to solve counting problems using the Fundamental Counting Principle, permutations, and combinations.
A deli offers 4 types of meat (ham, turkey, roast beef, and pastrami), 3 types of bread (white,
wheat, and rye), and 2 types of cheese (cheddar and Swiss). How many different
types of sandwiches can you make?
Tree Diagram
What relationship do you notice between the number of options of meat, bread, and cheese with the number of
different types of sandwiches?
If one event can occur in m ways and another event can occur in n ways, then the number of
ways that both events can occur is m • n.
This principle can be extended to 3 or more events as well.
Fundamental Counting Principle
In how many different ways can you order the letters A, B, and C?
6
Permutation - an ordering of n objects.
The number of permutations of n distinct objects is:
n!
factorial
n(n 1)(n 2)...321
** 0!1
Verify using your calculator.
The number of distinguishable permutations of n objects where one object is repeated q1 times, and another is repeated q2 times, and so on is:
Permutations with Repetitions
n!q1!q2!...qk!
Use the letters A, B, C, D, E, and F.
Combination - is a selection of r objects from a group of n objects where the order is not important.
Combinations of n Objects Taken r at a Time
The number of combinations of r objects taken from a group of n distinct objects is denoted by
nCr and is given by:
!!!rrn
nC
rn
Verify using your calculator.