Q.2. How many 4-digit numbers are there with no digit repeated?
The thousands place of 4-digit numbers has to be formed by using the digits 1 to 9(0 cannot be included).
Therefore, the number of ways in which thousands place can be filled is 9.
Hundreds,tens, unit place can be filled by any digits from 0 to 9.
The digit cannot be repeated in 4-digit numbers and thousand places is occupied with a digit.
Hundreds, tens, unit place can be filled by remaining any 9 digits.
Therefore, there will be as many 3-digit numbers as there are permutations of 9 different digits taken 3 at a time.
Therefore, the required number of 3-digit numbers
Thus, by multiplication principle, required 4 -digit numbers is