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
$$\left( \begin{array}{c}n\\ m \end{array} \right) = \frac{n!}{m! \, (n-m)!} = \frac{n \, (n-1) \dots (n-m+1)}{ m \, (m-1) \, (m-2) \dots 1}$$
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.

 

[tacman]

Sure, I'd be happy to help! Permutations, combinations, and variations can definitely be extended to include negative numbers. Let's go through each one and see how it would work with negative numbers:

1. Permutations: A permutation is an arrangement of objects where the order matters. In the case of negative numbers, we would still follow the same rules as we do with positive numbers. For example, if we have the set {-3, -2, -1}, the number of permutations of 2 elements would be 6, just like it would be for positive numbers. The only difference is that we would have negative numbers in our arrangements.

2. Combinations: A combination is a selection of objects where the order doesn't matter. Again, the rules for combinations would stay the same for negative numbers. For example, if we have the set {-3, -2, -1} and we want to find the number of combinations of 2 elements, it would be 3, just like it would be for positive numbers. The only difference is that we would have negative numbers in our selections.

3. Variations: A variation is similar to a permutation, but it allows for repetition of elements. For negative numbers, the rules would still be the same. For example, if we have the set {-3, -2, -1} and we want to find the number of variations of 2 elements, it would be 9, just like it would be for positive numbers. The only difference is that we would have negative numbers in our variations.

In summary, the definitions of permutations, combinations, and variations remain the same for negative numbers. The only difference is that we would have negative numbers included in our sets or arrangements. I hope this helps clarify things for you!