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This bank machine has four rows of buttons

1 2 3
4 5 6
7 8 9
0

Sam has a 4-digit bank number that uses one button from each row. For example his bank number could be 0571.
How many different possibilities for Sam's bank number are there?

The answer should be 648

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  1. 3 choices on each row except the last, so
    3*3*3*1

    That gives the number of digit choices. Now, for each choice of 4 digits, there are 4! ways to arrange them, so the final tally is

    3*3*3*1*4!

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