1. Homework Review
1. {SS, SNS, SNN, NSS, NSN, NN} 2. {SSS, SSNS, SSNNS, SSNNN, SNSS, SNSNS, SNSNN, SNNSS, SNNSN, SNNN, NSSS, NSSNS, NSSNN, NSNSS, NSNSN, NSNN, NNSSS, NNSSN, NNSN, NNN}
3) w2 = .30 4) w4 = ) a) b) c) 1 13) 1/12 or .083

2. Homework Review
23) Pass: 85% Fail/With: 15% 24a) {Underweight (U), extremely underweight (X), normal weight (N)} 24b) P(U) = .19, P(X) = .06, P(N) = .75
25) P($10) = .01, P($1000) = P($10000) = P($0) = ) P(Sales) = .55 P(not sales) = ) 6 36a) 1/3 36b) 1/2

3. Turn your Word Problem into the Bin

4. Homework Review
27a b. 1/36 27c. 1/4 28a. 4/9 28b. 5/9 29a b. 1/20 29c. 9/10
30. 3/ ; 1/ / /3; 1/2 37a b. 1/25 37c. 21/25

5. Permutations & Combinations
CLE Distinguish between and use permutations and combinations to solve problems

6. Factorials Symbolized by “!”
Means you multiply the given number by every number below it to 1
5! = 5 x 4 x 3 x 2 x 1
0! = 1
Can be done easily on a Graphing Calculator…

7. Permutation
A permutation is an ordered list of elements selected from a set. Two permutations are different unless they consist of exactly the same elements in exactly the same order
Follows from the Multiplication Principle we learned in Chapter 1
A city is divided into 3 districts to be surveyed by 5 employees. How many different ways can employees be assigned to the districts, assuming one per district?

8. Permutation Principle
The number of permutations of n distinct objects taken r at a time is:
P(n, r) = n!/(n – r)!
Can also be done easily on the calculator…

9. Permutation Problem
A director of a community theater is conducting auditions for a play which has 6 distinct roles: 4 for females and 2 for males. There are 7 females and 8 males trying out for their gender-specific roles. How many ways could the females be selected? How about the males? How many different casts could be made from the people trying out?

10. Permutation Problem
How many different 4-letter words can be formed from the letters of “math”?
How about “book”?
When letters repeat, divide by factorial of repeated letters…
How about “banana”?

11. Classwork/Homework Break
Work on p. 47 #1 – 15
Quiz tomorrow
Test on Thursday

12. Homework Review
1a b. 56 1c d a. 24 2b c d. 126 ;

13. Homework Review
; ; x

14. Combinations
Selecting a certain number of objects with no concern about order
A subset of r objects can be selected from a set of n distinct objects by:
C(n, r) = n!/[(n – r)! r!]
Once again, can be done easily on the calculator

15. Combinations Examples
There are 8 engineers qualified to serve on a design team. If the team is to consist of 5 engineers, how many possible teams can be created?
The core curriculum at Gigantic State University requires that each student takes 2 Humanities courses from a choice of 5 classes and 2 Science from a choice of 4 classes. Find the number of different course selections available

16. Comparison Between Permutations/Combinations
Order matters
Often used when looking for “positions” or “rank”
Order irrelevant
Often used when wanting to form a team or a choice

17. Classwork/Homework Worksheet
Quiz Tomorrow over Basic Probability, Permutations, and Combinations
Test Thursday