Practice with
Permutations and Combinations
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center


Answer the following questions dealing with permutations and combinations.
Grab your graphing calculator.

1. Determine whether the following situations would require calculating a permutation or a combination:

a.)  Selecting three students to attend a conference in Washington, D.C.
                          
permutation     combination

 

b.)  Selecting a lead and an understudy for a school play.
                          
permutation     combination

 

c.)  Assigning students to their seats on the first day of school.
                          
permutation     combination

 


 

2. Evaluate:  
Choose:

12
60
480
720

 

 

3. A teacher is making a multiple choice quiz.  She wants to give each student the same questions, but have each student's questions appear in a different order.  If there are twenty-seven students in the class, what is the least number of questions the quiz must contain?

 


   Answer

 

 

4. Which of the following is NOT equivalent to ?
Choose:

                                                   

 

 

5.

 A coach must choose five starters from a team of 12 players.  How many different ways can the coach choose the starters?
 

Answer

 

 

6.

The local Family Restaurant has a daily breakfast special in which the customer may choose one item from each of the following groups:
 

Breakfast Sandwich Accompaniments Juice
egg and ham
egg and bacon
egg and cheese
breakfast potatoes
apple slices
fresh fruit cup
pastry
orange
cranberry
tomato
apple
grape

a.)  How many different breakfast specials are possible?

b.)  How many different breakfast specials without meat are possible?

Answer 

 


 

7.

In how many ways can 3 different vases be arranged on a tray?
 

 

Answer 

 

 

8.

There are fourteen juniors and twenty-three seniors in the Service Club.  The club is to send four representatives to the State Conference.

a.)  How many different ways are there to select a group of four students to attend the conference?

b.)  If the members of the club decide to send two juniors and two seniors, how many different groupings are possible?

Answer 



 

9. If represents the number of combinations of n items taken r at a time,
what is the value of
when n=4?

Choose:

24                 14                  6                 4