How many numbers are there in all from 4000 to 4999 (both 4000 and 4999 included. having at least one of their digits repeated?
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Correct Answer: Option B
Explanation:
Total number of digits between 4000 and \(4999=1000\)
nos. when no digits are repeated \(=9^{\star} 8^{\star} 7=504\)
Now to verify, consider a four digit no. between 4000 and 4999t one's place \(=9\) digits can be used (only 4 cannot be used as it is used at 1000th place)t 10's place, 8 digits can be used at 100's place, 7 digits can be usedat 1000's place only one digit can be used(i.e.4 as the number should be between 4000 and 4999)
Numbers without repetition \(=1000-\left(9^{\star} 8^{\star} 7\right)=496\)
Total number of digits between 4000 and \(4999=1000\)
nos. when no digits are repeated \(=9^{\star} 8^{\star} 7=504\)
Now to verify, consider a four digit no. between 4000 and 4999t one's place \(=9\) digits can be used (only 4 cannot be used as it is used at 1000th place)t 10's place, 8 digits can be used at 100's place, 7 digits can be usedat 1000's place only one digit can be used(i.e.4 as the number should be between 4000 and 4999)
Numbers without repetition \(=1000-\left(9^{\star} 8^{\star} 7\right)=496\)