There are in all 10 digits, including zero. As the first digit of the number cannot be zero, so it can be chosen in 9 ways. Again, as a digit may occur any number of times in a number, the second, third and fourth digits of the numbers can be any one of the ten digits and so each of the remaining three places can be filled in 10 ways.
Hence the total number of 4-digit numbers = 9 × 103 = 9000.
Verification. All the 4-digit numbers will be between 1000 and 9999 and so their number is 9999 – 999 = 9000.
