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Here's the official formula:

The number of ways to CHOOSE n objects
taken
r at a time is

n C r  =  n! / ( n - r )! r!
 

* This can also be phrased as "how many combinations?"

Here are some other notations:

n C r  =  C n r  =  C( n , r )  =  ( n r )

"C" is for "choose"
(it's really "combinations")

This is NOT
a fraction!

Let's try it!

     You have 105 employees and you need to select a committee of
    
3.  How many ways can you do it?

* Ask yourself:  Does order matter?

NO!  So, use the choosing formula.

105 C 3  =  ( 105  3 )  =  105! / ( 105 - 3 )! 3!  =  105! / 102! 3!  =  ( 105 * 104 * 103 * 102! ) / 102! 3!  ...  the 102!'s cancel out  ...  =  ( 105 * 104 * 103 ) / 3 * 2 * 1  ...  the 3 * 2  reduces the 105 * 104 to 35 * 52  =  35 * 52 * 103  =  187,460