Question

A natural number is selected at random from $1$ to $1000.$ Then the probability that non-zero digits appear at most once is

• A. $\frac{11}{500}$
• B. $\frac{7}{250}$
• C. $\frac{4}{125}$
• D. $\frac{17}{750}$

Answer 1

The correct option is B $\frac{7}{250}$

Total ways $=1000$
Non-zero digits appear at most once means non-zero digits appear exactly once.
Favourable numbers $=\{1,2,3,4,\dots ,10,20,30,\dots ,100,200,300,\dots ,1000\}$
$\therefore$ Total favourable ways $=28$
$\therefore$ Required probability $=\frac{28}{1000}=\frac{7}{250}$