** **

quinn
Oct 9, 2014

#4**+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

#1**+5 **

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.

2) Your formula:

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

#2**0 **

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

#3**+10 **

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**+10 **

Best Answer

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