What is the probability of having a PIN number (digits $0$-$9$, starting with consecutive zeros allowed) with strictly increasing digits?
We easily deduce that, if $a_1, a_2, a_3, a_4$ are the respective digits, then $a_1<7, a_2<8$ and $a_3<9$. Moreover, I calculated that there are $7$ choices for $a_1$, ($7-a_1$) choices for $a_2$, ($8-a_2$) choices for $a_3$ and ($9-a_3$) choices for $a_4$ but I don't know how to proceed to the counting with all these variables. Finally, I know that this is ordered sampling without repetition but this doesn't seem to help. Thanks in advance!