Consider all possible dates (formatted DD/MM/YY) within a span of a century , from 01/01/01 to 31/12/00 (20th century!).
In this period there are N _k dates that can be expressed by k distinct digits, e.g. N₁=1 (11/11/11).

a. Derive the values of N _k for all other values of k (2 to 6).
b. What is the average k for the 20st century?
c. How about the 21st century?