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Solve by applying the counting principal. When using a four number PIN, how many different PINs are possible? a*b*c=___

I need help.. how do I work this? Step by step please.

The counting principle is oddly-named, since it mostly involves multiplying :-)

It just means that if you can do the first thing x ways, and then in the next step you can do that y ways, then overall you can do the whole thing in x * y ways.

Consider a two-digit PIN.

How many ways can you choose the first digit? 0 through 9 is ten digits, so that's 10 ways.

Choosing the second digit is the same. You can still choose any digit, including the one you picked for the first digit. This makes your second choice _independent_ of your first choice. Your first choice doesn't influence your second. So that's 10 ways.

So the counting principle says that you can choose a 2-digit PIN in 10 * 10 ways.

Move on to the third digit. Um, 10 ways again! This is getting familiar.

And the fourth?

And as a sanity check, consider that the PIN you must have chosen is an integer between or including 0000 through 9999. How many numbers is that?

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