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Factorial : n!/(nk)! = n(n1)(n2)...(nk+1)  why? 
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#1
Sep2010, 10:39 PM

P: 122

Why is the equation
(A) n!/(nk)! = n(n1)(n2)...(nk+1) true? For example, let n=4 and k=2, then 4!/2! = 4x3x2x1 / 2x1 = 4x3 = 12. I understand this example, but I can't make the connection with this and the righthandside of equation (A). For example, why is our example above not 4!/2! = 4(41)(42)...(42+1). I know this doesn't make any mathematical sense, but I can't understand how the equation on the righthandside of (A) is derived. Thanks for your help. M 


#2
Sep2010, 11:05 PM

Sci Advisor
HW Helper
Thanks
P: 25,228

The equation is an informal shorthand. You aren't supposed to include (n2) as a factor in the case where n=4 and k=2. You are supposed to STOP at (nk+1)=3.



#3
Sep2110, 02:48 AM

Admin
P: 23,594

Adding to what Dick wrote  it may become more obvious when you try to derive the equation.
[tex]\frac {n!} {(nk)!} = \frac {n \times (n1) \times (n2) \times ... \times (n  k + 1) \times (n  k) \times (n  k 1) \times ... \times 3 \times 2 \times 1} {(nk) \times (nk1) \times (nk2) \times ... \times 3 \times 2 \times 1} [/tex] Check what cancels out and what is left. And remember that when n and k are too small it is not possible to explicitly list all these terms. 


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