# Building a Burger

Pro Problems > Math > Statisics and Probabilities > Counting Principles## Building a Burger

I can have either mustard, ketchup, or relish for my burger. I can choose either swiss, Monterey, or cheddar cheese. I can choose either pickles, tomatoes, or lettuce. I can choose wheat bread or white (but I must have bread). I dislike the combination of mustard and swiss cheese. I like all other combinations, including combinations which include no cheese, condiments or veggies. How many combinations are there which I will like?

## Solution

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In a basket I have slips of paper with several different digits on them. In another basket I have slips of paper with several different letters on them. If I reach into the first basket and pull out a number, and then reach into the second basket and pull out a letter, there are 161 possible results. How many letters of the alphabet are *not *in the second basket?

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

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There are three buttons on a wall, each of which can be pressed or unpressed. There are four levers on the wall, and each of them can be either flipped up or down, or in a central position. How many possible arrangements of levers and buttons are there?

### Andy and Roger

Andy picks three letters from his name and arrange them on the table. Roger picks two letters from his name and arrange them. If Roger puts his two letters after Andy’s three letters, how many possible arrangements of five letters are there?

### Tic Tac Toe Grid

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For example, the following arrangement is valid, because the green is horizontally connected to the blue square, and the red square is diagonally connected to the green square.

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In how many different ways can the letters STOPS be arranged?

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Burger Heaven is the new restaurant in town, and they offer to make your burger however you want it, with the following possibilities:

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

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

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

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

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In how many ways can you arrange the digits?