Modeling Monday Follow Up The actual count of trees!

Teacher Old Trees New Trees

Loggins 1282 655

Fox 1280 660

Lindahl 1274 641

Averages: 1279 652

12.4 Permutations

Permutations

group of elements with order– ex: zip codes, phone #s

key words:– arrange– order– assign

order matters!

Remember??I have 5 positions and 5 people to fill

the positions

Make 5 blanks: 5 4 ∙ = 5!3 2 1∙ ∙∙

= 120

I have 4 people to choose from to fill 2 positions

Make 2 blanks:

For 2nd slot?

4How many choices for 1st slot?

3

4 3 = 12∙

Permutations Formula

Formula:

!

!n r

nP

n r

# of people to choose

from # you are arranging

Memorize!!

Permutations Formula

Last example using formula:

(4 people to choose from to fill 2 positions)

4!

4 2 !

4 2P

4!

2! 12

can put in calc

!

!n r

nP

n r

Remember: 8 cars parallel parked along one side of street.

How many ways can all 8 be arranged?

Three diff ways to solve:1) 8!

3)

68 7∙

= 40, 3202) 5 4∙ 3∙ 2 1∙∙ ∙ ∙

8 8P 8!

8 8 !

8!

0!

8!

1

How many if only 5 cars out of 8 arranged?

2 diff ways to solve:

2)

68 7∙1) 5 4∙ ∙ ∙ =

8 5P

8!

8 5 !

8!

3! 6720

6720

Example:

If we have 8 books, how many ways can we arrange 3 on a bookshelf?

Two methods:

OR

8 7 6∙ ∙ = 336

8 3P 8!

5! 336

Probability of getting a Permutation

a) How many possible perms are there? 5!= 120

A 5-letter perm. is selected at random from the letters GRATE.

=24b) How many of these perms BEGINS with G?

1 4 3 2 1

c) What’s the prob. the perm BEGINS with G?24 1

120 5

Probability of getting a Permutation

A 5-letter perm. is selected at random from the letters GRATE.

=63 1 2 1 16 1

120 20

d) What’s the prob. the 2nd letter is a T and last is a G?

e) What’s the prob. the 2nd letter is a consonant and last is a E?18 3

120 20

TOO: 11 girls try out for Varsity soccer.

a) In how many ways could the 11 positions be filled if there are no restrictions?

b) In how many ways can the positions be filled if Mabel must be goalie?

c) What’s the prob. that Mabel is goalie? d) What’s the prob. that Mabel, Sue or Deb is

goalie? e) What’s the prob. that Mabel, Sue or Deb is

goalie and Alice or Pat is center forward?

Arranging letters in a word with repeats

MISSISSIPPI

Total letters

Count repeating letters:4 - I’s

Total letters: 11

4 - S’s 2 - P’s11!

4!4!2! Divide by # of each repeat

= 34, 650

T.O.O.Arranging letters in a word with repeats

FOOTBALL

Total letters

Repeating letters:2 - O’s

Total letters: 8

2 - L’s8!

2!2! Divide by # of each repeat

= 10,080

Homework

Pg. 647-650 # 1-17 odd, 20, 21