Transcript Lesson # 64 – 65 Notes Permutations and Combinations

Lesson # 64 – 65 Notes
Permutations and Combinations
1. The Counting Principle – The number
of outcomes for an event is the product
of the number of outcomes for each
stage of the event.
Example :
Flip a coin and roll a number cube. The
coin has 2 sides, the cube has 6 sides.
The total number of possible outcomes is
2 x 6 = 12
Try this one 
Martha is selecting the menu for a banquet.
Her choices are:
entrée: chicken, beef, fish
salad: Caesar, house
side dish: rice, vegetables, pasta
dessert: cake, pie, ice cream
How many different meals of one entrée,
salad, side dish, and dessert could Martha
order?
Answer:
entrée: chicken, beef, fish = 3 choices
salad: Caesar, house = 2 choices
side dish: rice, vegetables, pasta = 3 choices
dessert: cake, pie, ice cream = 3 choices
3 x 2 x 3 x 3 = 54 choices
Factorial Notation –
2. The expression n! is the product of all
numbers starting with n and counting
backward to 1. The symbol for factorial is
the exclamation point. The expression “5!”
is read “five factorial.”

Example – 5! = 5 x 4 x 3 x 2 x 1 = 120
Try this one 
Kelly has 4 field day ribbons.
In how many ways can she display
all four of them on her wall?
Try this one 
Kelly has 4 field day ribbons.
In how many ways can she display
all four of them on her wall?
4 x 3 x 2 x 1 = 24
Permutation –
3. A permutation is an arrangement of a
set of objects in a particular order. You
can use the notation nPr to express the
number of permutations of n objects
chosen r at a time.
 Example – In a bag, there are 10 blocks
that are all different colors. In how many
different ways can you select 5 blocks?
 10P5 = 10 x 9 x 8 x 7 x 6 = 30,240 ways
Try this one 
Find the value of the expression.
6P3
Try this one 
Find the value of the expression.
6P3
6 x 5 x 4 = 120