I have a gut feeling that there's factorials involved in this, but I'm having trouble simplifying it.
If one rolls an N-sided die X amount of times, what would the formula be for determining the probability of there being no repeats?
Example: Roll a 10 sided die 4 times, the probability of there being no repeats is
$\frac{10}{10} * \frac{9}{10} * \frac{8}{10} * \frac{7}{10}=0.504$.
I thought that it should be $\frac{10! / 7!}{10^4}$.
But $\frac{10 * 9 * 8 * 7}{10^4} = 0.504$ and $\frac{\frac{10!}{7!}}{10^4} = 0.072$
You take away the factors by dividing. So instead of $10!-7!$, we have $10\cdot9\cdot8\cdot7=\frac{10!}{6!}$. I think that's enough for you to finish it from here ;)