Permutation and Combination Lesson

​Permutations and combinations

Fundamental Counting Principles

If decision M can be made ___m____ ways and decision N can be made ____n___ ways, then the two decisions can be made __m⋅n___ ways.

​Example 1

Example 2

Example 3

Multiple Choice

To enter their home, the Clayton family enters a 4-digit code. How many codes are possible?

• 16

• 1,000

• 10,000

• 100

Factorial = n!

Permutations

Permutations in desmos:

​nPr(n,r)

Permutations in desmos:

Multiple Choice

There are 16 players on the baseball team. How many ways can the coach make a 9-player batting order?

• 4,151,347,200

• 57,657,600

• 362,880

• No solution

Math Response

There are 28 students in Mr. Miller’s homeroom. How many ways can the students elect a student council representative and alternate?

Type answer here

Correct Answer: 756

Deg^°

Rad

Permutations w/ repetition:

​Must use factorial.

Multiple Select

How many different 9-letter arrangements are possible using the letters in the word DISAPPEAR?

• 9!/2!

• 9!/(2!2!)

• 90,720

• 181,440

Combination:

A group of objects in which _____order___ ___DOESN’T____ _matter_!

nCr =

n = total number of objects available

r = number of objects to use for the arrangement

Example 12

​Desmos: nCr(n,r)=value

Example 13

Example 14

Example 14

Multiple Choice

There are twelve employees at the sub shop. How many ways can the manager choose four for the Sunday evening shift?

• 11880

• 495

• 48

• 72

Multiple Choice

There are 85 players on the football team. How many ways can the coach choose three to represent the team in the coin toss?

• 9877

• 98770

• 98707

• 98077

Multiple Choice

How many ways can 4 candy bars be chosen from a store that sells 30 candy bars?

• Combination

• Permutation

Multiple Choice

How many ways can 13 students line up for lunch?

• Combination

• Permutation

Multiple Choice

How many ways can you make a 3-letter arrangements out of the letters in the word TRAPEZOID?

• Combination

• Permutation

Multiple Choice

How many ways can you choose 2 books from a shelf of 40 books?

• Combination

• Permutation

Multiple Choice

How many ways can 12 swimmers finish in first, second, and third place?

• Combination

• Permutation

Multiple Choice

How many ways can Ms. Mayette choose two students from 27 to help put away calculators at the end of class?

• Combination

• Permutation

Multiple Choice

You have enough tickets to play 6 different games at the amusement park. If there are 14 games, how many wats can you choose six?

• 2,162,160

• 3003

Multiple Choice

How many different ways can 9 trumpet players in the marching band line up?

• 36,288

• 362,880

Multiple Choice

Seven students worked together on a project. How many ways can their teacher choose four to present the project?

• 840

• 35

Assignment: you must join class and not a game!
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4th period: U556764
8th period: V737298

Assignment:
1.Basic Probability -quizizz
2.Permutation and Combination -Quizizz