Permutations Permutations and and

CombinationsCombinations

Standards:MM1D1b. Calculate and use simple permutations and combinations.

How many different lunches could you order if there were 4 different sandwiches, 3 different side orders and 4 different drinks?

How many different ice cream sundaes could you order if there were 3 different flavors of ice cream, 4 different sauces, and 2 different toppings?

Ice Cream Sundae

Chocolate

Strawberry

Pineapple

Caramel

Lunch

Suppose you wanted lunch and an ice cream sundae. What would you do?

Suppose you wanted either lunch or an ice cream sundae. What would you do?

Ice Cream Sundae

Chocolate

Strawberry

Pineapple

Caramel

Lunch

When using the counting principle,

the word “and” means to multiply.

x

When using the counting principle,

the word “or” means to add.

+

N factorial

For any positive integer n, the product of integers from 1 to n is called n factorial and is written as n!. The value of 0! Is defined to be 1.

Examples:1. 5!5 · 4 · 3 · 2 · 1 = 2. 9!9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 =

Permutations

A permutation is an arrangement of objects in which order is important. The number of permutations of n objects is given by nPn = n!. The number of permutations of n objects taken r at a time, where r ≤ n, is given by nPr = n!

(n – r)!

Example 1

You Try!!

Example 2

You Try!!

Example 3

You Try!!

Guided Practice

Guided Practice

Evaluate the expression.8. 4P3 9. 6P2 10. 7P4

Homework

Math 1 Textbook:

pg 344: 1 – 18 ALL

write problems and show all work!!

Combinations

A combination is a selection of objects in which order is NOT important. The number of combinations of n objects taken r at a time, where r ≤ n, is given by

nCr = n!

(n – r)! · r!

Example 1

Example 2

You Try!

Example 3

Example 3 cont…

You Try!

Homework

pg 349: 1 – 20 ALL

write problems and show all work!!