Activity for Counting and Permutations
 Topic Index | Algebra Index | Regents Exam Prep Center

 

Supplies:  3x5 cards labeled with various letters of the alphabet (no letters repeat).

R
A

I
N

 Directions:
1.  Students work in pairs (or groups).  Distribute a set of cards to each pair or group.  A set of cards should consist of 4 cards.  The task is to find all four-letter arrangements of the cards.  The arrangements do not have to spell actual words.  Ask students to record each "word".

2.  Encourage students to develop a strategy for finding their answers.  

3.  Discuss the findings with the class.

4.  When all possible four-letter combinations have been found, give each pair or group an additional card and ask them to find all possible five-letter combinations.

D
R
A

I
N

 

5.  Students could also be asked to make a tree diagram showing their findings.

This activity leads to discussions of tree diagrams, the counting principle, and permutations.  

 

As a follow-up activity, give each group of students a set of 4 cards where one of the letters repeats.

B
O

O
T

Distribute a set of cards to each pair or group.  As before, the task is to find all four-letter arrangements of the cards.  The arrangements do not have to spell actual words.  Ask students to record each "word".  Ask students to make observations about their answers. 
(While the permutation formula will yield the number of possible arrangements of the letters of BOOT, some of the arrangements will be the same.)