
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 18th, 2016, 03:17 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 03:25 AM. 
January 18th, 2016, 06:49 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,900 Thanks: 1094 Math Focus: Elementary mathematics and beyond 
Your approach and result are correct.


Tags 
license, plate 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Clarification on permutation of license plates?  DerGiLLster  Probability and Statistics  2  March 24th, 2015 06:36 PM 
A steel plate 2 cm thick is maintained at a temperatur  rsoy  Physics  0  November 14th, 2013 12:29 AM 
Calculate the inertia tensor of an offangle flat plate?  mrbiggl3s  Calculus  0  September 29th, 2011 04:42 AM 
Greedy Algorithm for license purchase problem  Shaitan00  Computer Science  6  November 17th, 2008 08:26 AM 