1.6 Probability & 6.7 Permutations and Combinations
So divinely is the world organized that every one of us, in our place and time, is in balance with everything else.

Experimental Probability: Based on observation of actual events, tests, or experiments.
P

Ex1) A player hit the bull’s eye on a circular dartboard 8 times out of 50.
Find the experimental probability that the player hits the bull’s eye.
P (bull's eye)

# of bull's eyes
# of total throws

8
50

4

25
0.16 or 16%

Theoretical Probability: Based on what would happen in theory.
P

Ex2) Find the theoretical probability of rolling a prime number when you roll a regular six-sided die.
P (odd)

# of prime numbers that can be rolled
# of numbers that can be rolled

3
6

1
2 or 50 %

A permutation is an arrangement of objects in a specific order.
Ex3) How many ways can 8 swimmers be assigned in 8 lanes?
Ex4) From a class of 25 students, how many ways can 4 students exit the classroom?
Ex5) Abby, Bart, Cara, Dean, and Erin are running for student council.
The offices are President, Vice President, and Secretary. How many ways can these five students fill the positions?

Number of permutations: The number of ways that n items can be arranged r at a time. ORDER MATTERS!
n
P r
 n !
 n
 r

!
P
Ex7) How many 4-letter codes can be made if no letter can be used twice? a) Method 1: Use the Multiplication Counting Principle.
b) Method 2: Use the permutation formula.

Number of combinations: The number of ways that n items can be arranged r at a time. ORDER DOES NOT
MATTER!
n
C r
 r !
n !
 n
 r

!
7
C
4
Divides out combinations that are the same items in a different order.
Ex9) A pasta bar offers 10 different add-ins. How many ways can you choose 4 add-ins for your pasta?

Ex10) You have 7 different textbooks. How many different ways can you arrange them on your shelf in your bedroom?
Ex 11) You have 6 friends. How many ways can you choose 4 of them to hang out with you?
Ex 12) A disk jockey wants to select 5 songs from a new CD that contains 12 songs. How many 5-song selections are possible?
Ex13) You want to hang 6 pictures in a row on a wall. You have 11 pictures from which to choose. How many picture arrangements are possible?

1.6 Probability & 6.7 Permutations and Combinations
So divinely is the world organized that every one of us, in our place and time, is in balance with everything else. pg. 42 #6-14 even, 17-20,
24, 25, 27, 28-33 pg. 348 #1-31 odd plus 18,
30, 32, 40, 46-49