Question

Find the total number of different 4-digit numbers using all the digits in the number 4129.

Answer 1

When repetition of digits is not allowed:
A four digit number has four places unit's, ten's, hundred's and thousand's.
Unit's place can be filled by any one of digit 4,1,2,9. So, unit's place can be filled in 4 ways.
Similarly, ten's place can be filled in 3 ways.
And, hundred's place can be filled in 2 ways.
And, thousand's place can be filled in 1 way
Thus, total number of required number = $4\times 3\times 2\times 1=24$