How many numbers are there in all from 4000 to 4999 (both 4000 and 4999 included. having at least one of their digits repeated?
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 \(=1000-\left(9^{\star} 8^{\star} 7\right)=496\)