Alg 2 - Permutations & Combinations

Permutations & Combinations - Alg 2

By Caleb Allen

An arrangement of [things] in a particular order.

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You can find the number of permutations in Desmos.

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• FUNCTIONS→NUMBER THEORY→nPr( )

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• 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.

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

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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)

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Combinations

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

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

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​Example:

Steps for Solving

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

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

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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​

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​