Counting License Plates

Try to answer the following:​  In the Kingdom of Mathlandia, all license plates consist of 3 letters, followed by 4 numbers.  For example, one possible license plate is ABC-1234.

​Try to answer the following:

1.  How many unique license plates are possible?
​2.  Suppose no license plate is allowed to use the letter "O".  How many license plates are possible?
​3.  Suppose no repetitions are allowed--which means that no letter or number can be used more than once.  How many license plates are possible?
4.  Suppose no repetitions are allowed, and the letter "M" has to be used.  How many license plates are possible?
5.  Suppose repetitions ARE allowed, but the sequence 211 is NOT allowed.  How many license plates are possible?

You will find the solution here.

To Ponder On Your Own:  Would the answer to number 5 change if the disallowed sequence was 111 instead of 211?

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