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 Combinations formula question, is this right?? Please check

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So using the formula nCr=n!/[(n-r)!*r!] I have 18C3= 18!/[15!*3!] upon entering it into the calculator I get 816, which is the answer. When I do it by hand, I keep getting  1,632.  So I do 18C3= 18!/(15!*3!) = (18*17*16)/(3) cancelling out the 15's in the denominator and numerator and I get 1,632. Can someone please tell me what Im doing wrong?! I've been stuck with this, I must be really missing something. Thanks in advance for the help.

 Sep 27, 2016

6+0 Answers

 #1
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18C3= 18!/(15!*3!) = (18*17*16)/(3*2)   Note that the denominator has 3! not just 3  (3! = 3*2)

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 Sep 27, 2016
 #2
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How does 3! = 3*2 ?

 Sep 27, 2016
 #5
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With the factorial sign, 3! means 3*2*1 or just 3*2, by definition.

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Alan  Sep 27, 2016
 #3
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How does 3! = 3*2 ?

 

3! = 3*2*1 or just 3*2

 Sep 27, 2016
 #6
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You must understand what (!), or "factorial symbol" means!!. So,

10! means =10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

100! means=100 x 99 x 98 x 97.......all the way down to 1. Got it?.
 

 Sep 27, 2016
 #7
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Okay, thanks everyone you have cleared up the fog! What would a full credit solution look like with all the steps for this?

 Sep 27, 2016

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