# Buttons and Levers

Pro Problems > Math > Statisics and Probabilities > Counting Principles## Buttons and Levers

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?

## Solution

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

### Guitar Pickin'

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[No calculators, please]

### 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.

In how many different ways could the three squares be placed on the grid?

### Making License Plates

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

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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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How many different ways could I have Thanksgiving Dinner?

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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!"

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