# Making License Plates

Pro Problems > Math > Statisics and Probabilities > Counting Principles## Making License Plates

In the State of Confusion, all car license plates are made with the following stipulations:

- The license plate will have six characters.
- The first character will be a digit between one and nine inclusive.
- The next two characters will be digits between zero and nine inclusive.
- The fourth character will be a vowel
- The fifth character will be a consonant
- The sixth character could be any letter.

How many different license plates are possible in the State of Confusion?

## Solution

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Joan and Gene each order a burger. Joan says to the waiter, "I hate cheese, and I don't like romaine lettuce, but other than that, I'll take it however you feel like preparing it. Surprise me!"

Gene says to the waiter, "I want my burger well done, and with mustard and ketchup. Other than that, I don't care how it's prepared - surprise me!"

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Day One: 1 partridge in a pear tree

Day Two: 2 turtle doves *and *1 partridge in a pear tree

Day Three: 3 calling birds, 2 turtle doves, and 1 partridge in a pear tree

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After Mrs. Claus heard the elves singing this song one Christmas, she decided that the next year she would take this song to the extreme, and extend it to 20 days of Christmas, giving gifts (in the same pattern as the song) for 20 days.

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By how many gifts did Santa "outgive" Mrs. Claus?

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For Thanksgiving, I will have either have ham or turkey.

If I have turkey, I will have either potatoes or stuffing.

If I have ham, I will have either potatoes or rice.

If I have potatoes, I will have either green beans or peas.

If I have rice, I will have either peas or carrots.

If I have stuffing, I will have either carrots or green beans.

If I have green beans, I could have cranberry sauce with it.

If I don't have grean beans, I could have green bean casserole.

If I don't have peas, I can choose to have spinach.

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If I have ice cream, I could either have chocolate sauce or whipped topping on it, or put nothing on it.

If I have pie, I can choose mince, lemon meringue, cherry, or apple.

How many different ways could I have Thanksgiving Dinner?

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[No calculators, please]

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