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April 16th, 2013, 02:15 PM  #1 
Member Joined: Feb 2013 Posts: 44 Thanks: 0  weird probability problem...
Suppose Texas l;icense plates consist of 7 characters. The first two being letters of the alphabet. The next 3 being numbers and the last two being letters. Example of a license plate: AB123CD Determine the total number that can be created if..... a) There are no restrictions b) No letter may be repeated c) The digits in characters 4 and 5 may not contain the digit zero d) the digits in characters 4 and 5 may no contain the digit zero and the letter 0 may not be used. This whole problem is a little intimidating for me. This is part of the review for my test tomorrow. I had to pic my sister up from the air port so my buddy sent me a pic of the review, but he wasn't paying attention so he didn't get any of the answers.... anyways. Here's me taking a stab at this. a) c(26,2) c(10, 3) c(26, 2) b) c(26,2) c(10,3) c(24,2) c) c(26,2) c(10, 1) c(9,2) c(26, 2) d) c(25,2) c(10,1) c(9,2) c (25,2) 
April 16th, 2013, 02:54 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,822 Thanks: 723  Re: weird probability problem...
You are making a fundamental error (I assume that c( , ) means combination). You should not be dividing by 2, since order matters. For example: the answer to (a) is 26^2 x 10^3 x 26^2.

April 16th, 2013, 02:58 PM  #3 
Member Joined: Feb 2013 Posts: 44 Thanks: 0  Re: weird probability problem...
Hmmm thanks for the insight mathman! So what you're saying is b) 25^2 X 10^3 X 24^2 c) 26^2 x 10^1 x 9^2 x 26^2 d) 25^2 x 10^1 x 9^2 x 25^2 ????? And yes I was using the combination formula. Probably would have been wise for me to mention that.. 
April 16th, 2013, 03:15 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: weird probability problem..
I would simply use the fundamental counting principle to answer these questions. a) How many character choices do you have for each digit? 
April 16th, 2013, 03:20 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: weird probability problem...
I have merged your duplicate topics...you see what happened because you posted twice? I wasted my time, and my time is valuable, at least to me. Please pick the most appropriate subforum for your topic and post it only once. This avoids redundancy and duplication of effort on the part of our contributors. 
April 16th, 2013, 04:10 PM  #6 
Member Joined: Feb 2013 Posts: 44 Thanks: 0  Re: weird probability problem...
Sorry about that mark :/ I posted it in high school section first and figured that not many high schoolers would respond. Won't happen again, promise 
April 17th, 2013, 12:03 PM  #7  
Global Moderator Joined: May 2007 Posts: 6,822 Thanks: 723  Re: weird probability problem... Quote:
 

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