I'm new to factorial equations and wanted to see if I got it down properly.
I have 35 possible numbers, so N = 35.
I have 36 possible length, so R = 36.
This is a combinations where numbers can be in any order and duplicated.
So, using $(N + R - 1)!/R!(N-1)$ will give me $70!/36!34.$
This ends up giving me 1.1978571669969891796072783721689e+100/1.2647773110856641393911981237128e+43 and an answer of 9.4708938601117709521284466743182e+56.
Did I do this correctly or am I way off?
Let us represent the sequence as so $\square \square \square \dots \square$.
There are $36$ empty spaces. However, in each space there are $35$ possible numbers we can put there. So the value should be $35 \times 35 \times \dots \times 35=35^{36}$.
We generally use factorials when the elements in the sequence are distinct.
However, in this problem since each value can be used more than once(as pointed out in your comment), we should use the power $a^b$.
Generally, if there are $a$ elements of the length $b$ and all elements are can be used only once, then there are $\frac{a!}{(a-b)!}$ combinations.
However, if there are $a$ elements of the length $b$ and all elements are can be used more than once, then there are $a^b$ combinations.