Expert: Steve Holleran - 4/20/2007

Question
Steve:
Can you tell me how many combinations there are for numbers 1-999, in sets of three, as in a simple combination lock for a bike..1,2,3/1,2,4,/ 1,2,5, etc. Randy

Answer
Hi Randy,

This is a straightforward combinations calculation.  You are interested in finding the combination  

                  999 C 3

It can be done on a scientific calculator directly, and the answer is 165,668,499.

If you don't have a scientific or graphing calculator, the formula is :

 999 C 3 = 999! / (3! * 996!) which can be done as

       (999 * 998 * 997 * 996!) / (3 * 2 * 1 * 996!)

and you can see the 996! cancels out, then just compute the rest.

Steve Holleran