Answer and Explanation:
Given,
4 digits and 10 digits.
Firstly, we have to find that when it repeats the digit then
- First position code would be filled in by Three methods that is 3, 4, or 5.
- Second position code would be filled in by Ten methods.
- Third position code would also be filled in by Ten methods.
- Fourth position code would be filled in by 9 way but 0 is rejected.
- So, the total numbers of methods in the following case is [tex]3\times10\times10\times 9=2700[/tex].
Then, we have to find that when it not repeats the digit then
- First position code would be filled in by Three methods that is 3, 4, or 5.
- Second position code would be filled in by Nine methods in which one is reserved earlier.
- Third position code would be filled in by Eight methods in which two are reserved earlier.
- Fourth position code would be filled in by Six methods in which three are reserved earlier.
- So, the total numbers of methods in the following case is [tex]3\times9\times8\times6=1296[/tex]
