My Math Forum weird probability problem...

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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 sub-forum 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
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Re: weird probability problem...

Quote:
 Originally Posted by hamburgertime 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..
c) and d) look ok. b) should be 26 x 25 x 10^3 x 24 x 23.

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