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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
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B
120
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C
210
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D
90
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Solution

## The correct option is C 210The 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. ∴ The number of 2 digit numbers =5×6=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. ∴ The number of 3 digit numbers =5×6×6=180 ∴ Total number of numbers = 30 + 180 = 210

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