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# In a trail,supposea lawyer wants 2 men and 5 womento make up a special panel. so the formlar is nCr=n!/[r!*(n-r)]!,right?So,5C2=5!/[2!(5-2)]

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## can someone prove my method whether true or false?if true , why it equal to the original formula?

quinn  Oct 9, 2014

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There is a function called the Gamma function, defined as follows:

$$\Gamma (t)=\int_{0}^{\infty}x^{t-1}e^{-x}dx$$

When t is a positive integer this is equal to (n - 1)! but the Gamma function is defined for all values of t, so it is sometimes thought of as the extended factorial function.

So 5.6! would be calculated from Γ(6.6) (≈ 344.702...)   (5! = 120,  6! = 720)

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Alan  Oct 9, 2014
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I see two parts to you question:

1)  If you want 2 men and 5 women, you wouldn't use 5C2;  5C2 represents the number of ways that you can        choose a set of 2 out of a set of 5;  this does not represent choosing 2 men and 5 women.

nCr  =  n! / [ r! · (n-r)! ]

The  (n-r)!  in the denominator cancels all the factors in the numerator starting with (n-r) down through 1;        leaving only  n · (n-1) · (n-2) · ... · (n-r+2) · (n-r+1).

There is still a factor of  r!  in the denominator.

I agree with your process EXCEPT I feel that you need one fewer term in the numerator, because the (n-r)        factor gets cancelled also; in the numerator, stop with factor (n-r+1).

geno3141  Oct 9, 2014
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okay the original question is In a trilsupose a lawyerwants 2 men and 5 womento make up a special panel.if the 7 panel  menbers are selected at random fro a pool of 12 peoples,which istheprobality that the  lawyer will not get the desired panel?(sorry for i didnt write the question completelyand i got the anwser）

ok i got it know.Thank you for your help.

why 0!=1? can n be a negative or fraction in n! ?why or why not?

quinn  Oct 9, 2014
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Hi Quinn,

I have heard of an extended definition of factorial that does allow this but I have never used it.

From my knowledge base factorials belong to whole positive integers and 0 only.

5! means 1*2*3*4*5

What would 5.6! mean?    It means nothing to me.

Melody  Oct 9, 2014
#4
+27228
+10

There is a function called the Gamma function, defined as follows:

$$\Gamma (t)=\int_{0}^{\infty}x^{t-1}e^{-x}dx$$

When t is a positive integer this is equal to (n - 1)! but the Gamma function is defined for all values of t, so it is sometimes thought of as the extended factorial function.

So 5.6! would be calculated from Γ(6.6) (≈ 344.702...)   (5! = 120,  6! = 720)

.

Alan  Oct 9, 2014
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+94106
0

Thanks Alan,  I knew this existed but I have never used it.  :)

http://www.wolframalpha.com/input/?i=gamma%20function

Melody  Oct 9, 2014
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okay! Thank you,guys.

quinn  Oct 10, 2014