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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? - Mathematics

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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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Solution

Since the number is less than 1000, it means that it is a three-digit number, a two-digit number or a single-digit number.
Three-digit numbers:
The hundred's place can be filled by 5 digits neglecting zero as it can't be zero.
The ten's place and the unit's place can be filled by 6  digits.
So, total number of three digit numbers = `5xx6xx6=180`

Two-digit numbers:
The ten's place can be filled by 5 digits, except zero.

The unit's digit can be filled by 6 digits.
Total two digit numbers =`5xx6=30`

Single digit numbers are 1, 2, 3, 4, 5 as 0 is not a natural number. Thus, on neglecting it, we get 5 numbers.
Total required numbers =`180+30+5=215`

Concept: Permutations
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 39 | Page 16

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