How many variations of the numbers 1 - 45 can you make using 7 numbers?

Using factorials/permutations:

factorials: n!/(n-r)!
where n=45 and r=7

= 228713284800.00

https://en.wikipedia.org/wiki/Factorial

I'm not a mathematician, so I'm not guaranteeing this!

45x44x43x42x41x40x39= 228713284800

Same thing as Arlington said, permutations.

To explain: You have 45 choices of numbers. You have 7 spots to fill with numbers. First spot you have 45 options x next spot which is 44 options x next spot 43 options.

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

The answer depends on exactly what you mean by 'variations'. If the order in which the numbers are written matters, then the calculation of 45P7 already suggested is correct.

BUT

If you are applying this to some kind of lottery (I recognise the number 45 from watching Tattslotto draws), you actually need to use combinations rather than permutations, since the order in which the numbers appears is not relevant. If you are really asking "How many combinations of 7 different numbers can be created if the numbers are selected from a total of 45 numbers?", the answer is 45C7, which is calculated as 45!/(38! x 7!) = 45 379 620. The answer is much smaller because duplicates are ignored. That is, 1234567 is the same as 1324567, 1423567, etc. When you calculate the permutation, you treat these as separate answers.

https://en.wikipedia.org/wiki/Permutation
https://en.wikipedia.org/wiki/Combination