6th Grade Math Textbook, Fundamentals

Student A

Is First

Student B

Is First

Student C

Is First

Student D

Is First

ABCD

ABDC

ACBD

ACDB

ADBC

ADCB

BCDA

BCAD

BDAC

BDCA

BACD

BADC

CABD

CADB

CBAD

CBDA

CDAB

CDBA

DABC

DACB

DBCA

DBAC

DCAB

DCBA

 &KDSWHU

12-7

Permutations

Objective To determine the number of permutations of objects

Four students are standing in line at lunch. In how many
different ways can the four students stand in line?

To find how many different ways, find the number
of permutations for four students.

A is an arrangement of items or objects

in which order is important.

To determine the number of possible permutations, you can use

an organized list, a tree diagram, or the Fundamental Counting

Principle. Sometimes, but not always, you can use factorials.

Here are two ways to solve the problem above.

Method 1 Make an Organized List

Let A, B, C, and D represent the four students.

permutation

Remember:In a permutation,

the order matters!

Remember:A factorialof a number, n, is

the product of all positive integers less

than or equal to n. It is symbolized by n!,

which is read as “nfactorial.”

There are 24 different orders.

Method 2 Use the Fundamental Counting Principle

There are four different students standing in line at lunch. Any of

the four students could be first in line. After the first person in line

is determined, there are three students left who could be second in

line. After the second person in line is established, there are two

students left who could be third in line, and finally one student left

to be last in line.

1st 2nd 3rd 4th

Position Position Position Position

4 choices • 3 choices • 2 choices • 1 choice

Number of ways to stand in line: 4! 4 • 3 • 2 • 1  24

So there are 24 different ways for the four students

to line up at lunch.