Can someone show me why the following works out? Thanks!

C(5,5) = (5!) ÷ (5!)(5-5)!

= (5!) ÷ (5!)(0)!

= 5x4x3x2x1 ÷ (5x4x3x2x1)... (Thinking)?

The calculator says this equals 1.

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- Dec 9th 2008, 07:18 PMyvonnehr[SOLVED] dividing by 0!
Can someone show me why the following works out? Thanks!

C(5,5) = (5!) ÷ (5!)(5-5)!

= (5!) ÷ (5!)(0)!

= 5x4x3x2x1 ÷ (5x4x3x2x1)... (Thinking)?

The calculator says this equals 1. - Dec 9th 2008, 07:40 PMTruthbetold
I don't recall why but 0! = 1.

- Dec 9th 2008, 07:55 PMmeymathis

which is an empty product. An empty sum is 0. An empty product is 1. See this - Dec 9th 2008, 08:35 PMyvonnehra proof
Thanks, I will definitely look at this after my final! (Nerd)

- Dec 9th 2008, 09:43 PMChris L T521
- Dec 9th 2008, 09:48 PMyvonnehrmore research to do
Thanks! Looks like I have some more research to do after Finals.

Best of luck on your finals!

I just have two left to do, Prob & Stats, and Dynamical Systems! Thank goodness this semester is almost over!!!(Rock) - Dec 9th 2008, 11:10 PMmr fantastic
- Dec 10th 2008, 06:49 AMyvonnehr
- Dec 10th 2008, 05:43 PMawkward
You have already seen several excellent reasons why we define 0! = 1, but here is one more.

A fundamental recurrence relation for the factorial function is

We would like this recurrence to hold even when . This requires

- Dec 10th 2008, 08:50 PMyvonnehrvery nice!