Ascending Order Numbers Formation

To form a number with distinct digits in ascending order from the 9 non-zero digits, any subset of $k$ digits uniquely forms 1 such number. Total subsets of size $k$ from 9 digits = $\binom{9}{k}$. Total possible non-empty subsets = $2^9 - 1 = 511$. Subsets of size 0: 1 (empty set) Subsets of size 1: $\binom{9}{1} = 9$. Subsets of size $\ge 2$: $511 - 9 = 502$.