Question

How many 4-digit personal identification numbers are possible if the number cannot contain a zero?

Answer 1

The answer is: 6,561 possible identification numbers if the numbers can be repeated and 3,024 possibilities if the numbers cannot be repeated.

Step-by-step explanation:

If your number cannot include 0 (only 1 - 9), but numbers can be repeated, then all the digits have 9 different possibilities. To calculate the total number of possibilities you must multiply 9 x 9 x 9 x 9 = 6,561 different possibilities.

If the numbers cannot be repeated, then you would need to calculate 9! = 9 x 8 x 7 x 6 = 3,024 different possibilities.

Answer 2

If the pin is to be a 4-digit number and is not to contain any zero, there are 9 possible number in each of the digit. Those numbers are from 1 to 9. To determine the number of possible combination,
possible combination = 9 x 9 x 9 x 9 = 6561
Thus, there are 6561 ways to unlock.