I need help from a mathematics/statistics wiz here:

I need to know how to calculate the total number of possible
variations, based on the number of variables given.

For example:

Let's say I have ten (10) numbers:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Given these ten (10) variables, what are the total number of "ways"
(iterations) these numbers can be listed?

For example:

#1 -  1, 2, 3, 4, 5, 6, 7, 8, 9, 10
#2 -  1, 9, 8, 7, 6, 5, 4, 3, 2, 10
#3 -  9, 8, 7, 5, 6, 3, 4, 1, 2, 10

And so on.

Is it 10 to the 10th power? Or something else?

Also, in the example above, there were only 10 variables, but what I
want to know is the formula for calculating the total number of
possible iterations given "X" number of variables.

So that I can calculate the number of possible variations for any
given number of variables.

Thanks!

You are asking for the number of permutations of X things taken X at a
time. The answer is X! (X factorial = 1*2*3*4.....(X-1)*X)

You can see this pretty easily by thinking about it for the case X=10:

There are ten possibilities for the first number
There are nine possibilites for the second number, since one number
has already been used.

Thus, there are 10*9 = 90 possibilities for the first two numbers

There are eight possibilities for the third number, since two of the
numbers have already been used.

Seven possibilities for the fourth number, etc., etc. By the time you
get to the tenth number, there is only one possibility left. Thus the
total number of permutations of 10 things taken 10 at a time is:

10*9*8*7*6*5*4*3*2*1 = 10!