Alg 2 - Permutations & Combinations

Permutations & Combinations - Alg 2

By Caleb Allen

An arrangement of [things] in a particular order.

​​

You can find the number of permutations in Desmos.

​

• FUNCTIONS→NUMBER THEORY→nPr( )

  ​

• In the parenthesis enter (total number of items, number of items being chosen)

Permutations​

There are 7 people running a race. The top 3 win gold, silver, and bronze respectively.

​

So there are nPr(7,3)=​210 different possible ways to create a podium of the top 3.​

​

n is the number of things to select from

r is the number of things being selected and arranged​

Example:

A combination is a collection of things in which order does NOT matter.

You can find the number ofcombinations using DESMOS.

• FUNCTIONS 🡪NUMBER THEORY🡪nCr( )

• In the parenthesis enter (total number of items, number of items being chosen)

​

Combinations

​

In a class of 20 students, the teacher wants to make a group of 3.

​

There are nCr(20,3)=​1140 ways to make a group of 3 students.

​

​Example:

Steps for Solving

1. Decide if the problem is a permutation or a combination.

   ​

2. Identify the n (total number of items) and the r (number of items chosen)

   ​

3. Plug into calculator.

Practice Examples:

As a class

Example 1:

Running a Race

There are five people in a race.  Prizes are awarded for different places:  $50 for 1st place, $25 for 2nd and $15 for 3rd.  How many different ways can the prizes be awarded?

Example 2:

Running a Race

There are five people in a race.  Each of the top 3 finishers will receive $25.  How many different ways will the prizes be awarded?

Your Turn

2 problems​

Fill in the Blanks

For a certain experiment, four students were randomly selected from a class of 20.  How many different groups of four students are possible?

Fill in the Blanks

You are forming a 10-person committee from 9 women and 12 men.  The committee must consist of 5 women and 5 men.  How many different 10-member committees are possible?

Example 3:

Marbles

A bag contains 3 red, 5 green and 8 blue marbles.  How many ways can 2 red, 1 green and 2 blue marbles be chosen?

Your Turn

6 problems​

Fill in the Blanks

A 10-person student council will be selected from 18 students at a school.  How many possibilities are there for this student council?

Fill in the Blanks

The school board has seven members

The board must have three officers: a chairperson, an assistant chairperson, and a secretary.  How many different sets of these officers can be formed from this board?

Fill in the Blanks

The school board has seven members

How many three-person committees can be formed from this board?

Fill in the Blanks

To open your locker, you must dial a sequence of three numbers called the lock’s combination.  Given that there are 40 numbers on a lock, how many different locker combinations are there?

Fill in the Blanks

Suppose fifteen people qualify for a college cheerleading squad,

six women and nine men.

How many six-member squads can be selected?

Fill in the Blanks

Suppose fifteen people qualify for a college cheerleading squad,

six women and nine men.

Suppose that exactly two members of the six-member squad must be male. 

How many six-member squads can be selected?