# Difference between revisions of "2006 AMC 10A Problems/Problem 18"

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So, there are <math>5</math> choices for position. | So, there are <math>5</math> choices for position. | ||

− | Therefore there are <math> 5\times 10^4\times 26^2 </math> distinct license plates <math> \Rightarrow C </math> | + | Therefore there are <math> 5\times 10^4\times 26^2 </math> distinct license plates <math> \Rightarrow (C) </math> |

== See Also == | == See Also == | ||

*[[2006 AMC 10A Problems]] | *[[2006 AMC 10A Problems]] |

## Revision as of 21:12, 22 July 2006

## Problem

A license plate in a certain state consists of 4 digits, not necessarily distinct, and 2 letters, also not necessarily distinct. These six characters may appear in any order, except that the two letters must appear next to each other. How many distinct license plates are possible?

## Solution

There are ways to choose 4 digits.

There are ways to choose the 2 letters.

For the letters to be next to each other, they can be the 1st and 2nd, 2nd and 3rd, 3rd and 4th, 4th and 5th, or the 5th and 6th characters. So, there are choices for position.

Therefore there are distinct license plates