Why is 0! 1?
Date: 09/14/97 at 23:19:27 From: Kimberly Subject: Zerofactoro1 My question is: Why is zerofactoro 1? I've looked in encyclopedia and my math book, but I can't seem to find the answer. Please help me. Thank you for your time.
Date: 09/15/97 at 14:30:17 From: Doctor Statman Subject: Re: Zerofactoro1 Hi Kimberly, Here is a mathematical reason for 0! to be 1. Let's count how many ways there are to get 3 heads (H) and 2 tails (T) out of 5 tosses of a coin. Let's write down all the possibilities: HHHTT There are 10 sequences of 3 heads and 2 tails. Instead HHTTH of writing them all down, we could have calculated: HTTHH 5!/(3!2!) = 120/(6*2) = 10 TTHHH HHTHT HTHTH THTHH HTHHT THHTH THHHT Let's do the same thing for 4 heads and 1 tail: HHHHT There are 5 ways, and this matches 5!/(4!1!) = 120/24 = 5 HHHTH HHTHH HTHHH THHHH There is only one way to get all 5 heads, and that is HHHHH Now the formula would say 5!/(5!0!) and if 0! is anything other then 1 then this answer would not be equal to 1, as it should be. This formula is called a binomial coefficient. It means that if you want to choose r objects from n objects, and you don't care about the order of the r objects, then the number of ways to do that is n!/r!(n-r)! Hope this helps - write back if you want to talk about it some more. Sincerely, Doctor Statman -Doctor Statman, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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