Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Order.
A positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. Find number of ascending positive integers are there.
Integers
Digits
Order
Answer: is 502.
AIME I, 1992, Question 2
Elementary Number Theory by David Burton
There are nine digits that we use 1,2,3,4,5,6,7,8,9.
Here each digit may or may not be present.
\(\Rightarrow 2^{9}\)=512 potential ascending numbers, one for subset of {1,2,3,4,5,6,7,8,9}
Subtracting empty set and single digit set
=512-10
=502.
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