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. Answer

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).

Remember: The permutation formula takes order into account. The outcome (red, blue, green) is not the same as the outcome (green, blue, red.)

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.  Answer

How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?  Answer

How many different ways can four books be arranged on a shelf if they are selected from eight books?  Answer

When some of the items are identical, a different permutation formula must be used.

Use this permutation formula when some of the item possibilities are alike. If there are n items with n1 alike, n2 alike, n3 alike, . . ., nk alike, the number of permutations is calculated by dividing n factorial by the product of the factorials of the number of occurences of each of the like items.

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 . . . .   Answer

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?   Answer

Test your understanding of Permutations.
Practice Problems