Counting - Permutation and Combinations

Counting - Permutation and Combinations

By Caleb Allen*

​*Getting a 6/9 or better on this lesson will get you a 5 point participation grade

Factorial

Multiply a number by all whole numbers between it and 1.

​

How Many Ways to Arange 5 Cards

​

​That means that the number of ways is:

​First choice has 5 possibilities

​Second choice has 4

Third choice has 3​

and so on...​

​

A permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters

Definition:

How many was are there to arange r things out of n things?

​

The number of ways to arange things​

Permutations

​ We have 27 and are arranging 3

​

Permutations

Calculator

Directions​

​

1. Type in the n value

2. Press MATH

3. Move over to PRB​

4. Select nPr

5. Type in rthe r value

Example

Given a class of 15 students and a front row of 5 seats, how many different ways could students be arranged in the front row assuming all seats are filled?

This is a permutation

Combinations

How many ways to select r objects from n objects:

Smaller than nPr (we are dividing by r!)

​

1. ​Type in the value of n

2. Press MATH

3. Move over to PRB or PROB

4. ​Move down to nCr or press 3

5. ​Type in the value of r

6. Press enter​

​

Calculator

Example:

How many different 5 hard hands are there for a 52 card deck?

Some More Problems

See if you can get these​

Multiple Choice

"The student body of 165 students wants to elect three representatives". Is this a permutation, combination, or neither?

• Combination

• Neither

• Permutation

Multiple Choice

From a box of 16 color crayons, you select 4 as your favorites. How many different ways can you make this selection?

• 64

• 43,680

• 1820

• 20

Multiple Choice

The value of 5! is ____.

• 25
• 15
• 120
• 720

Multiple Choice

What is the value of ₅P₂?

• 60
• 10
• 20
• 15

Multiple Choice

A team of 17 volleyball players needs to choose three players to refill the water cooler.  How many different ways can the players be chosen?  

• 3360
• 560
• 4080
• 680