Permutations

Linear and Circular

Essential Question:

• How do I solve problems using permutations?

Fast Facts…

• A permutation is an arrangement of objects in a specific order.

• When objects are arranged in a row, the permutation is linear.

• When objects are arranged around a circle, the permutation is circular.

• “!” (factorial): means multiply by everything less than a number

Continued…

• 4! = 4•3•2•1 = 24• Calculator: MATH PRB !• To find the number of linear permutations,

use the formula P=n!• To find the number of linear permutations of

“n” objects taken “r” at a time use:

!Pr

( )!

nn

n r

Example 1 and 2

• Solve:8P3 =

= 6 3

4 3

P

P

Example 3

• Find the number of permutations for the first 5 letters of the alphabet for each situation:– Taken 2 at a time

= 205 2P

Circular Permutations

• To find the number of Circular Permutations use the formula: Pc = (n-1)!

Example 4

• 7 different pairs of sunglasses are on a circular display rack. How many ways can the display rack be set up?

• Pc = (7-1)!• Pc = (6)!• 720

Identical Objects

• To find the number of permutations with identical objects use the formula:

11 2

!

( ! !...)

nP

r r

Example 5

• Find the number of permutations with identical objects of the letters in each word:

• ALGEBRA BASEBALL

• 2520 5040

7!

2!8!

(2!2!2!)

Assignment

• Pages 640-641, #’s 9-50 all