pin guessing

If you have ever wondered how many tries it would take to guess a four-digit PIN at an automated teller machine, here is the answer and how it is calculated.

We are trying to arrange the numbers. There are 10 numbers to arrange, zero to nine. There are only four spaces, or slots, for each number. In the first space, place a 10 because there are 10 numbers; in the second space, place a nine; in the third space, place an eight; and in the fourth space, place a seven. Multiply 10 times nine times eight times seven.
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The total number of all such possible passcodes is 10∗9∗8∗7=5040.

Following is a demonstration of the solution. The difference between the demonstration and four-digit PIN guessing is that we have 10 numbers to choose from, not four letters, as in the demonstration.  Note that 0! = 1.

In every math session I have tutored, we did not do any New Math. One student showed me some New Math, and we solved the problem the old way. Ha!