I'm challenging myself to figure out the mathematical expression of the number of possible combinations for certain parameters, and frankly I have no idea how.
The rules are these:
Take numbers 1...n. Given m places, and with no repeated digits, how many combinations of those numbers can be made?
- 1 for n=1, m=1 --> 1
- 2 for n=2, m=1 --> 1, 2
- 2 for n=2, m=2 --> 12, 21
- 3 for n=3, m=1 --> 1,2,3
- 6 for n=3, m=2 --> 12,13,21,23,31,32
- 6 for n=3, m=3 --> 123,132,213,231,312,321
I cannot find a way to express the left hand value. Can you guide me in the steps to figuring this out?