Difference between revisions of "2006 AMC 10A Problems/Problem 18"
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Therefore, the number of distinct license plates is <math> 5\times 10^4\times 26^2 \Longrightarrow \mathrm{C}</math>. | Therefore, the number of distinct license plates is <math> 5\times 10^4\times 26^2 \Longrightarrow \mathrm{C}</math>. | ||
| − | == Video | + | == Video Solutions == |
https://youtu.be/3MiGotKnC_U?t=1446 | https://youtu.be/3MiGotKnC_U?t=1446 | ||
~ThePuzzlr | ~ThePuzzlr | ||
| + | |||
== Video Solution == | == Video Solution == | ||
https://youtu.be/0W3VmFp55cM?t=847 | https://youtu.be/0W3VmFp55cM?t=847 | ||
Revision as of 08:06, 19 December 2021
Problem
A license plate in a certain state consists of 
digits, not necessarily distinct, and 
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 the position of the letters.
Therefore, the number of distinct license plates is 
.
Video Solutions
https://youtu.be/3MiGotKnC_U?t=1446
~ThePuzzlr
Video Solution
https://youtu.be/0W3VmFp55cM?t=847
~ pi_is_3.14
Video Solution
~savannahsolver
See also
| 2006 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
