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Question

# How many numbers lying between 100 and 10,000 can be formed with the digits 1,2,3,4,5, if atleast one digit in the same numbers are repeated?

A
7505P35P4
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B
7505P3+5P4
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C
750+5P35P4
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D
750+5P3+5P4
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Solution

## The correct option is A 750−5P3−5P4Total no. of 3 digit numbers formed=5×5×5=125Total no. of 4 digit numbers =5×5×5×5=625∴ Total numbers between 100 & 1000 formed =750.Total number of 3 digit numbers without repetition=5P3No. of 4 digit numbers without repetition=5P4∴ No. of numbers between 100 & 1000 with at least one repeating digit=750−5P3−5P4

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