Can someone show me why the following works out? Thanks! C(5,5) = (5!) ÷ (5!)(5-5)! = (5!) ÷ (5!)(0)! = 5x4x3x2x1 ÷ (5x4x3x2x1)... ? The calculator says this equals 1.
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I don't recall why but 0! = 1.
which is an empty product. An empty sum is 0. An empty product is 1. See this
Thanks, I will definitely look at this after my final!
Originally Posted by Truthbetold I don't recall why but 0! = 1. This is one of the reasons: In calculus, there is something known as the Gamma Function. It is defined as follows: When evaluating , where , it has this special property: Now, let's see what happens when This means that By definition, Thus,
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!!!
Originally Posted by yvonnehr 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!!! At your level: 0! = 1 by definition so that the number of way of choosing zero objects from n objects is equal to 1 (a highly sensible result).
Originally Posted by mr fantastic At your level: 0! = 1 by definition so that the number of way of choosing zero objects from n objects is equal to 1 (a highly sensible result). Very sensible! Thank you!
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
Originally Posted by awkward 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 This worked out very nicely!
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