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January 18th, 2016, 02:17 AM   #1
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license plate

Suppose a state's license plate contains 6 letters on it where the letters can be repeated. What is the probability that a license plate will contain the letters USA (in that order) somewhere in the six letters?

My attempt:

Total number of possible license plates = 26*26*26*26*26*26 = 26^6

The letters USA can appear as
1. USA _ _ _ This has 26*26*26 possibilities
2. _ USA _ _ This also has 26*26*26 possibilities
3. _ _ USA _ This also has 26*26*26 possibilities
4. _ _ _ USA This also has 26*26*26 possibilities

So, the total number of possibilities with USA in it = 4(26^3)

Therefore, the probability that a license plate will have USA = (4(26^3))/26^6

Am I correct? Is there a better way to solve this? Thanks.

Last edited by shunya; January 18th, 2016 at 02:25 AM.
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January 18th, 2016, 05:49 AM   #2
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Your approach and result are correct.
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