Question

5. A security lock pass-number is to contain 4 numbers using the digits 0 through 9. The 0 is NOT to be the first digit, no digit is repeated, and the last digit must be 9. How many of these pass-numbers can be created?

Answer 1

First slot: 9 possibilities (1-9, since 0 can't be used)
Second slot: 9 possibilities (0-9, other than the number used in the first slot)
Third slot: 9 possibilities (same reasoning as second slot, except that it can't be the same as second slot)
Fourth slot: 1 possibility (has to be a 9)

Total number of possibilities: \(9\cdot9\cdot9\cdot1=\cdots\)

Answer 2

8 options for the first digit (1-8, no zero or 9)
8 options in the second (0-8, but without whatever you used in the first slot)
7 options for the third (0-8, but without whatever you used in the 1st and 2nd slots)
1 option for the last on (9)
8*8*7*1=448