# L8.Permutations and Repetition

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```					Name: ____________________________________                                   Date: __________________
Permutations and Repetition
Algebra 1
As we saw in the last homework problem from yesterday’s lesson, when elements of a set repeat our
counting technique must be modified. How to do this is illustrated in the next two exercises.

Exercise #1: How many arrangements are there of all the letters in the word LINEAR?

Exercise #2: Consider the letters in the word BEEPER.

(a) How many arrangements are there of these 6-letters if each of the 3-E’s is considered to be
different?

(b) How many different ways can you rearrange just the 3-E’s?

(c) How many total ways are there of rearranging the letters in the word BEEPER if the 3-E’s are
considered to be the same?

Exercise #3: Consider the word ASPARAGUS.

(a) How many arrangements of these 9-letters would be possible if they were all different?

(b) How many arrangements are there of the repeated letters?

(c) How many total distinct arrangements of the letters in this word can be made?

Algebra 1, Unit #11 – Sets and Counting – L8
The Arlington Algebra Project, LaGrangeville, NY 12540
Exercise #4: Find the total number of ways of rearranging the letters in the following words. Express

(c) TENNESSEE                                            (d) CALCULATE

Exercise #5: What is the total number of distinct 4 digit numerals that can be formed using the digits
from the year 2001?

Exercise #6: The greatest number of different 5-letter arrangements can be made from the letters in
which of the following words? Why? {Hint: Think before you calculate!}

(1) ANGLE                           (3) ORDER

Exercise #7: Jonathan would like to make an 8-digit code from all of the numerals in his birth date. If
he was born on 12/28/1982 (December 28th, 1982), how many different 8-digit codes could he create?

Algebra 1, Unit #11 – Sets and Counting – L8
The Arlington Algebra Project, LaGrangeville, NY 12540
Name: ____________________________________                                   Date: __________________
Permutations and Repetition
Algebra 1 Homework

Skills
For problems 1 through 12, find the total number of arrangements of the letters in the following words.
Express your answer in both factorial notation and as a whole number.

1. CALCULUS                                         2. PAPA                  3. NONSENSE

4. PEPPER                                           5. SCISSORS              6. PARALLEL

7. MURMUR                                           8. VOODOO                9. MISSISSIPPI

10. SYSTEM                                          11. NONSENSE             12. BOOKKEEPER

Algebra 1, Unit #11 – Sets and Counting – L8
The Arlington Algebra Project, LaGrangeville, NY 12540
13. How many different arrangements are there of the numerals in the year 1999?

(1) 12                              (3) 2
(2) 24                              (4) 4

14. Which of the following represents the number of different arrangements of the numerals in the year
2002?

4!
(1) 4!                              (3)
2! 2!
4!
(2)                                 (4) 4 P2
4!

Applications
15. Principal Brooks would like to assign each student at Arlington High School with a 7-digit code
made from the seven digits in the school’s phone number, 486-4860. If there are 3,200 students in
the high school, will Mr. Brooks have enough codes? Numerically justify your answer.

16. Would Principal Brooks have enough 10-digit codes if he also included the area code of 845?

Reasoning
17. The greatest number of different 6-letter arrangements can be made from the letters in which of the
following words?

(1) PASSES                          (3) DIVIDE

18. In how many different ways can 5 pennies, 4 nickels and 6 dimes be given to 15 children so that
each child receives exactly 1 coin? {Hint: Think about how this is similar to the problems already
done in this section.}

Algebra 1, Unit #11 – Sets and Counting – L8
The Arlington Algebra Project, LaGrangeville, NY 12540

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