1. Discrete Math Section 15.3 Solve problems using permutations and combinations
Read page 578
Combinations and permutations are used to select a smaller set (subset) from a larger set of elements.
Permutations are used when the order of the elements is important. Combinations are used when the order of the elements is not important.

2. Permutations Combinations nCr = n!___ (n – r)! r! nPr = n!___ (n – r)!
Used to choose r items out of a set of n items
Combinations
nCr = n!___
(n – r)! r!
Used to choose r items out of a set of n items

3. For a certain raffle, 845 tickets are sold.
a. In how many ways can four $50 gift certificates be awarded?
b. In how many ways can a $100, a $50, a $20, and a $10 gift
certificate be awarded?
a. 845C4 = 845 ! 845−4 ! =
b. 845P4 = 845 ! 845−4 ! 4! =
x 1010
x 1011

4. A calculator used to evaluate permutations and combinations
TI evaluate 7P3
type “7”
MATH
PRB
nPr
Type “3”
ENTER
TI Nspire
Scratch pad
Calculate
Menu
Probability
Permutations
nPr(7,3)

5. In how many ways can a hand of five cards be dealt from a 52 card deck?
Order does not matter…. 52C5 = 2,598,960

6. The science club has 24 members
The science club has 24 members. A president, secretary, and treasurer are to be elected. In how many ways can the three officers be elected?
Order is important… 24P3 =

7. Assignment
Page 580
Problems 2,3,4,6,8,10,15,17,20