Probability, Permutations,

& CombinationsLESSON 11.1

Objective

• Define probability

• Use the counting principle

• Know the difference between combination and

permutation

• Find probability

Probability

PROBABILITY: the measure of the likeliness of an event

# 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡𝑜 𝑤𝑖𝑛

# 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡𝑜 𝑝𝑙𝑎𝑦

Probability

1a. What is the probability of rolling a 4 on a 6-sided

die?

1b. What is the probability of rolling an even number

on a 6-sided die?

Probability

2. A bag of candy contains 12 red, 11 yellow, 5

green, 6 orange, 5 blue, and 16 brown candies.

a.) What is the probability that you will randomly draw a yellow

candy from the bag?

b.) What is the probability that you will NOT draw an orange candy

from the bag?

Sample Space

Sample Space is a visual representation of all possible outcomes.

3a. We are going to flip a coin 3 times. Find the

sample space.

Sample Space

3b. How many outcomes give us at least 2 heads?

3c. Find the probability of getting at least 2 heads.

Permutation & Combination

If a sample set is too large to list, the number of

outcomes and successes can be determined using

permutations and combinations.

Permutations – ORDER MATTERS

Combinations – order DOES NOT matter

Permutation

Permutation – ORDER MATTERS

To calculate the number of permutations, multiply

the number of choices possible for each position.

This is called the Counting Principle.

Permutation

4a. On a 3-question multiple choice quiz, how many

different quizzes could be turned in if there are 4

options (a,b,c,d)?

4b. How many different quizzes could be turned in if

no answers were repeated?

Permutation

To calculate permutation without repetition:

𝑛𝑃𝑟 = 𝑃 𝑛, 𝑟 =𝑛!

𝑛 − 𝑟 !where “n” is the number of objects to choose from

and “r” is the number of object being selected.

Permutation

Permutations can be calculated with a calculator.

a) Type the value of “n”

b) [MATH] → PRB → nPr

c) Type the value of “r” and press enter

TRY IT!

5a. P(5,3) b. P(16,5) c. P(25,13)

Combination

Combination – order DOES NOT matter,

*object may be repeated

𝑛𝐶𝑟 = 𝐶 𝑛, 𝑟 =𝑛!

𝑛 − 𝑟 ! 𝑟!

Combination

Combinations can be calculated with a calculator.

a) Type the value of “n”

b) [MATH] → PRB → nCr

c) Type the value of “r” and press enter

TRY IT!

6a. C(5,3) b. C(16,5) c. C(25,13)

Combination

7. Mrs. Mann is picking 4 students to be team

leaders. There are 25 students in the class. How

many different ways can she pick the 4 students?

Combination

8. Super Generic Ice Cream Shoppe has 9 different

flavors to put in your ice cream. You can choose 3

flavors to put in a single dish. How many different

flavor combinations can you create?

Permutation & Combination

Permutation OR Combination

9 a. Arrangement of 10 books on a shelf

b. Committee of 3 people out of a group of 10

c. Class presidency – 1st is president, 2nd is VP, etc.

d. Draw a hand of 6 cards from a deck of cards

e. Number of ways to make a license plate

Permutation & Combination

THINK!

• Identify if order matters or doesn’t matter FIRST

• Permutations can use the counting principle,

combinations don’t

• Generally: Two things at once – Combination

One after the other - Permutation

Permutation & Combination

10. There are 6 students presenting projects in a

history class. The teacher is randomly determining

the order in which the students will present. Each

student only presents once. Brooke is one of the six

students. What is the probability that Brooke will

present first?

Compound Probabilities

If more then 1 event is happening, it creates a

Compound Probability.

If independent - P A𝑎𝑛𝑑B = P A ⋅ P(B)

If dependent - P A𝑎𝑛𝑑B = P A ⋅ P(B𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔A)

Compound Probabilities

11. From a deck of 52 cards, 3 cards are randomly

chosen. They are a 10, Jack, and another 10, in that

order.

a. Find the probability that this event occurs if each

card is replaced after drawn.

b. Find the probability that this even occurs if each

card is NOT replaced each time.

Probability

12. The table bellow lists the items in Jana’s closet.

She randomly selects 2 items. What is the probability

that she will select 2 shirts?

ItemNumber of Each Color

Black Blue White Red Purple

Shirt 2 3 1 5 5

Shoes 3 0 1 2 2

Probability

13. There are 4 nickels, 3 dimes, and 5 quarters in a

purse. Find the probability.

a. P(1 dime, then 1 nickel, then another dime)

without replacement

b. P(drawing 3 coins and getting 1 of each)

Homework

Worksheet 11.1