Name: 
 

AII.12 - Permutations and Combinations



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1 

Which of the following scenarios represents a combination?
a.
The arrangement of 8 books on a shelf.
b.
The number of ways 6 people can be seated at a round table if 2 people must be seated next to each other.
c.
The letters r,s,t,v,w are used to form 5-letter passwords for a security system.
d.
A seven person committee selected from the junior class.
 

 2 

Twelve runners are in a cross country race.  How many different ways can they finish first, second, and third?
a.
2200
b.
1320
c.
220
d.
132
 

 3 

Select all of the following that represent a permutation.

I.    There are 10 dogs racing for first and second prize.   How many possible outcomes are there?
II.   Six speakers are scheduled to address a group of College students.   In how many different orders can the speakers appear?
III.  How many 6 letter words can we make using the letters in the word LIBERTY?
IV.   How many different committees of 5 people may be formed from 10 people?
V.    A password consists of 4 different letters of the alphabet.  How many possible passwords are there?
VI.   How many triangles can you make using 6 non collinear points on a plane?
a.
I, II, III, V
b.
I, V, VI
c.
II, IV, VI
d.
I, II, V, VI
 

Short Answer
 

 4 

Directions: Type in your answer.  Enter your answer as a whole number.

A store owner employs a total of 3 cashiers and 7 clerks.  The owner plans to select a committee of 1 cashier and 2 clerks.  What is the number of different committees the owner could choose?
 

 5 

Directions:  Type in your answer.  Your answer must be an integer.

A family reunion planning committee with 8 members plans to elect 3 officers - a present, treasurer, and historian.  If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?
 

 6 

Twenty horses compete in a race.  In how many ways could the horses have finished in first place through third place?
 

 7 

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



 
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