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Question

# How many 4 digit numbers are there, when a digit may be repeated any number of times?

A

104

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B

3 x 43

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C

9 x 103

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D

410

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Solution

## The correct option is C 9 x 103 In a four digit number 0 cannot be placed at thousand's place. So thousand's place can be filled with any digit from 1 to 9. Thus thousand's place can be filled in 9 ways. Since repetition of digits is allowed, therefore each of the remaining 3 places can be filled in 10 ways by using the digits from 0 to 9. Hence, the required number of numbers = 9 x 10 x 10 x 10 = 9 x103

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