Your iPad has a 4 digit passcode. How many different passcodes are possible, if the digits can repeat?

Question

 I got 210 but my teacher said that was incorrect. What am I doing wrong?

Answer 1

This is a permutation problem because the order matters.  Within each of the pass codes digits you have ten choices (0 through 9).  You can do that for each of the four digits getting 10⁴ = 10,000 possible pass codes.  Here's another way to look at it.  The smallest possible pass code is 0000.  The largest one is 9999.  You can have every pass code between 0000 and 9999, a total of 10,000 pass codes.