Permutations, combinations and variations of negative numbers.

[sutupidmath]

need help on this?

well guys i was doing some problems with series and i cam up with this problem, i think it belongs to combinatorics but i'll post it here.
How is defined the permutations, combinations and variatons of negative numbers. For example if you were required to find the combinations of -2 elements taken from a set of n elements. TO me this makes no sens?

$$\left(\begin{array}{cc}-2\\&n)$$

any help would be appreciated

p.s. sorry for my latex, but i do not know how to write this.

 

[Chris Hillman]

Zero. Or not

How is defined the permutations, combinations and variatons of negative numbers. For example ...$\left( {\small \begin{array}{c}n \\ -2 \end{array} } \right)$

The standard answer is zero, but if you simply plug a negative value for m (or a value exceeding n) into the formula
$$\left( \begin{array}{c}n\\ m \end{array} \right) = \frac{n!}{m! \, (n-m)!}<br /> = \frac{n \, (n-1) \dots (n-m+1)}{ m \, (m-1) \, (m-2) \dots 1}$$
you get nonsense. See this and this for some musings which should intrigue you!

p.s. sorry for my latex, but i do not know how to write this.

Try hitting "reply" and look at the LaTeX markup in the window.