Permutations

A permutation is a collection of distinct objects arranged in a specific order. 
An important distinction of permutation is that order of the objects is important. 
 
Example:  When creating license plates for automobiles, the order of the letters and numbers used is important.  However when dealing cards for some card games, the order of the cards dealt does not matter. 

The statistical application includes the number of permutations that can be formed using 'r' different objects selected from a set of 'n' distinct objects and is notated by  nPr  and is calculated by   n! / (n - r)! 

Both calculators have the permutation operation available under the MATH PRB menu. 

Steps for calculating the permutation of 'n' objects taken 'r' at a time: 

1. Press the actual number of objects that represent 'n'.  Caution:  The entry of the 'n' must be keyed into the calculator before the permutation operation is activated. 

2. To access the permutation menu, press , , , and .  The choice 2:nPr will bring the operation to the cursor position on the display of the calculator. 

3. Press the actual number of objects that represent 'r'. The display should look like this, except with the numbers entered in place of 'n' and 'r'. 
n   nPr   r 

4. Press  and the result will be displayed on the next line. 
 

Example:  To calculate the number of ways that a group of eight finalists in an art contest are to be awarded three prizes - first, second, and third, use a permutation calculation. 

Solution: Since the prizes are ordered, this is a permutation of n = 8 different people, taken r = 3 at a time.  Use the calculator to find the answer to 
8  nPr  3.    The correct answer is 336 different possible ways of awarding the three prizes.