A book has 999 pages. If a page is opened at random the probability that the sum of the digits in its number is 9, is

Total number of cases = 999

Favorable cases.

The page number can be with all identical digits, i.e. _{$333\to 1$}

The identical and one different like 009, 117, 225 and 441 _{$\to 4\times \frac{3!}{2!}=12$}

All different digits like 018,027,036,045,126,135,234 _{$\to 7\times 3!=42$}

So favorable cases= 55

Desired probability =_{$\frac{55}{999}$}