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Let $x$ be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then $\mathrm{x}$ is equal to
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Verified Answer
The correct answer is:
2481
Number of numbers between 2999 and 8001 $=8001-2999-1=5001$
Number ofnumbers with all digitdistinct and having
as starting digit
Number ofnumbers with all digitdistinct and having 4 as starting digi $4=50$
Similarly number of numbers with starting digit 5,6 and 7 respectively are 504,504 and 504 . Total numbers $=5 \times 504=2520$
Hence, required number $=5001-2520=2481$
Number ofnumbers with all digitdistinct and having
as starting digit
Number ofnumbers with all digitdistinct and having 4 as starting digi $4=50$
Similarly number of numbers with starting digit 5,6 and 7 respectively are 504,504 and 504 . Total numbers $=5 \times 504=2520$
Hence, required number $=5001-2520=2481$
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