Do Now1. Find the number of permutations with 7

books taken 4 at a time.2. Find the number of permutations of the

letters in each word:

Tennessee Georgia Alabama

Pg. 640-641; 9-50 all

9. 4,92010. 69611. 212. 213. 5614. 21015. 2016. 72017. 604,80018. 210

19. 5020. 1,00021. 13222. .0723. 60,48024. 43,243,20025. 6,72026. 33627. 1,68028. 20,160

Continued…

29. 830. 40,32031. 40,32032. 362,88033. 1,814,40034. 259,459,20035. 13,366,08036. 96,909,12037. 271,252,80038. 427,518,000

39. 72040. 72041. 6042. 36043. 10,08044. 10,08045. 151,20046. 34,65047. 908,107,20048. 24

Continued…again…

49. 72050. 24

Combinations

Essential Question:How do I solve problems

involving combinations?

Formula:

!

!( )!n r

nC

r n r

Things you need to know:In a permutation, ORDER

matters. In a combination, order does NOT matter.

The value of combinations will be less than most permutations.

You will use the nCr function in the calculator.

Problem Types:Determine the values for “n” (total

number of objects) and “r” (the rate the objects are taken). “n” is always larger.

Multiply the combinations together using the nCr key if there is more than one type of object.

Find the probability of an event by dividing the product of individual combinations by the total number of combinations. Your answer is a %.

Example 1Find the # of ways to purchase 3

different kinds of juice from a selection of 10 different juices. (The order in which they are chosen doesn’t matter, making this a combination).

10C3 = 120

Example 2The difference between a permutation and

a combination:COMBO: How many ways are there to

choose a committee of 3 people from a group of 5?

5C3 = 10Permutation: How many ways are there to

choose 3 separate office holders (chairman, secretary, and treasurer) from a group of 5?

5P3 = 60

Example 3How many different ways are

there to purchase 2 CD’s, 3 cassettes, and 1 videotape from 7 CD titles, 5 cassette titles, and 3 videotape titles?

7C2 • 5C3 • 3C1 =

630

Example 4In a recent survey of 25 voters, 17

favor a new city regulation and 8 oppose it. Find the probability that in a random sample of 6 respondents from this survey, exactly 2 favor the proposal regulation, and 4 oppose it.

.0537 = 5.4%

17 2 8 4

25 6

C C

C

Assignment:Pg. 647, #’s 4-39a.

Pg. 647, 4-39a

4. 1265. 220 / 13206. 28007. 7.6%8. 359. 7010. 12011. 12612. 913. 11

14. 115. 116. 7517. 50418. .00519. .05320. 1021. 822. 49523. 21024. 225,792,840

Continued…

25. 15,50426. 25227. 37828. 37829. 25230. 53.6%31. 26.8%32. 42.9%33. 17.9%

34. Combo35. Combo36. Permutation37. Permutation38. Permutation39. 2,598,960