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January 18th, 2016, 02:17 AM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 422 Thanks: 18  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. 
January 18th, 2016, 05:49 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond 
Your approach and result are correct.


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