Combinations

A combination is a collection of distinct objects arranged without respect for specific order.  An important distinction of combination is that order of the objects is not important. 
 
Example:  When a department has thirty (30) members and a committee of seven (7) members is needed to carry out a task or study, the question of how to create the committee does not involve the concept of order.  However when creating license plates for automobiles, the order of the letters and numbers used is important. 

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

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

Steps for calculating the combination 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 combination operation is activated. 

2. To access the combination menu, press , , , and .  The choice 3: nCr 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   nCr   r 

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

Example:  To calculate the number of ways that a committee of seven (7) members can be formed from a department of thirty (30) employees , use a combination calculation. 

Solution: Since the committee membership is not concerned with order, this is a combination of n = 30 different people, taken r = 7 at a time.  Use the calculator to find the answer to   30  nCr  7. 
The correct answer is 2,035,800 different possible ways of creating a committee of seven (7) members from a department of thirty (30) members.