MATHCOUNTS TOOLBOX

Facts, Formulas and Tricks

Lesson 11:Permutations

Consider the possible arrangements of the letters a, b, and c.  List the outcomes

in the sample space. If the order is important, then each arrangement is a

permutation of the three letters

Consider the possible arrangements of the letters a, b, and c.  List the outcomes

in the sample space. If the order is important, then each arrangement is a

permutation of the three letters

Outcomes in the sample space.

abc    acb    bac     bca    cab    cba

There are six permutations.

Permutation Formula:Use when the item possibilities are all

different.n: number of available items or choices

r: the number of items to be selected    Sometimes this formula is written:

P(n,r).

If n = 5 and r = 2, what is the value of 5P2? The symbol 5P2 means the number of

permutations of 5 items taken 2 at a time. 

If n = 5 and r = 2, what is the value of 5P2? The symbol 5P2 means the number of

permutations of 5 items taken 2 at a time. 

A permutation of 5 objects taken 2 at a time is equal to . . .

If n = 5 and r = 2, what is the value of 5P2? The symbol 5P2 means the number of

permutations of 5 items taken 2 at a time. 

A permutation of 5 objects taken 2 at a time is equal to . . .

How many permutations are there for the letters in the word, BANANA?

First, notice there are six total letters of which the A is repeated 3 times and the N

is repeated 2 times. The number of permutations is equal to . . . . 

How many permutations are there for the letters in the word, BANANA?

First, notice there are six total letters of which the A is repeated 3 times and the N

is repeated 2 times. The number of permutations is equal to . . . . 

There are six letters in BANANA (6!).The A repeats three times (3!)

and the N repeats two times (2!).There are 60 permutations.

How many permutations are there for the letters in the word, BANANA?

First, notice there are six total letters of which the A is repeated 3 times and the N

is repeated 2 times. The number of permutations is equal to . . . . 

There are six letters in BANANA (6!).The A repeats three times (3!)

and the N repeats two times (2!).There are 60 permutations.

How many permutations are there for the letters in the word, HAPPY?

Remember to ask yourself, how many total letters are there?  How many letters are

repeated? How many times is each letter repeated? 

How many permutations are there for the letters in the word, HAPPY?

Remember to ask yourself, how many total letters are there?  How many letters are

repeated? How many times is each letter repeated? 

There are five letters in HAPPY (5!).The P repeats two times (2!).

There are

How many permutations are there for the letters in the word, HAPPY?

Remember to ask yourself, how many total letters are there?  How many letters are

repeated? How many times is each letter repeated? 

There are five letters in HAPPY (5!).The P repeats two times (2!).

There are

1) Calculate the value of 7P3

1) Calculate the value of 7P3

A permutation of 7 objects taken 3 ata time is equal to . . .

1) Calculate the value of 7P3

A permutation of 7 objects taken 3 ata time is equal to . . .

2) Calculate the value of 9P4

2) Calculate the value of 9P4

A permutation of 9 objects taken 4 at a time is equal to . . .

2) Calculate the value of 9P4

A permutation of 9 objects taken 4 at a time is equal to . . .

How many permutations are there for the letters in the word,

STATISTICS?

How many permutations are there for the letters in the word,

STATISTICS?

There are ten letters in STATISTICS (10!).

How many permutations are there for the letters in the word,

STATISTICS?

There are ten letters in STATISTICS (10!).

The S repeats three times (3!),the T repeats three times (3!),

and the I repeats two times (2!).

How many permutations are there for the letters in the word,

STATISTICS?

There are ten letters in STATISTICS (10!).

The S repeats three times (3!),the T repeats three times (3!),

and the I repeats two times (2!).

Fini!