Question

Find the number of possible choices for a 3-digit PIN (personal identification number) if the digits cannot be repeated.

Answer 1

The pin must have $3$ digits, which are different. The first place in the pin can be any one of $0-9$. Thus, there are $10$ possibilities for the first place. The second place has all the possibilities, except the digit used in the first place. Thus, there are $9$ possibilities for the second place. Using a similar logic, there are $8$ possibilities for the third place. Thus, in total, there are $10\times 9\times 8=720$ possible 3-digit PINs.