# How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?

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How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?

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To find: number of natural numbers less than 1000 that can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times

For forming a 3 digit number less than 1000 possible ways are:

5 × 6 × 6…(in 100’s place 5 digits are only possible 0 not included.) =180

For forming a 2 digit number less than 1000 possible ways are:

5 × 6……(in 10’s place 5 digits are only possible 0 not included.) = 30

For forming a 1 digit number less than 1000 possible ways are:

5…(0 not included because it is a whole number and natural number is asked in question.)

So total number of numbers less than 1000 that can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times=180 + 30 + 5 = 215