The counting principle & permutations

mochaeris

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May 28, 2013
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A license plate is to consist of three digits followed by two uppercase letters. Determine the number of different license plates possible if repetition of numbers and letters is not permitted.





Can someone please solve this problem and show your work? I'm stumped:(

Thanks,
Monique
 
Have you seen any examples of the Fundamental Counting Principle?

Here is a short video. Please watch the lesson, and then tell us what part(s) you do not understand.

In your exercise, the different events are:

Picking a first digit
Picking a second digit
Picking a third digit
Picking a first letter
Picking a second letter

You need to think about the number of possible outcomes (no repeats), for each of these five events, and then multiply those five numbers together.

How many different outcomes are possible, for picking a first digit?

After a first digit is chosen, how many outcomes remain for picking a second digit?

And, then, picking a third digit ... How many outcomes are possible for that?

How many different outcomes are there for picking a first letter?

After a first letter is chosen, how many outcomes remain for picking the second letter?

The Fundamental Counting Principle says that multiplying these five event counts gives the total number of license plates possible.

If you're still stuck, specific questions are best. Cheers :cool:
 
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