Question

How many numbers lying between 9 and 1000 that can be formed with the digits 0, 1, 2, 3, 7, 8 (numbers can be repeated)?

• A. 30
• B. 120
• C. 210
• D. 90

Answer 1

The correct option is C 210

The numbers lying between 9 and 1000 consist of 2 or 3 digits in which repetitions are allowed.
Case 1. (For two digit numbers)
As the tens place can be filled by only non - zero digits and unit digit can be filled up in 6 ways.
$\therefore$ The number of 2 digit numbers $=5\times 6=30$
Case 2. (For three digit numbers)
Hundreds place can be filled up with only non-zero digits hence it can be done in 5 ways and the rest of the places i.e., tens and unit places can be filled up in 6 ways each.
$\therefore$ The number of 3 digit numbers $=5\times 6\times 6=180$
$\therefore$ Total number of numbers = 30 + 180 = 210