<p>Anybody know of a resource where I can improve my ability in this topic area?</p>
<p>look up probability chapters in a statistics book or ap statistics prep book...</p>
<p>Hey man, not to discourage you, but I have the exact same problem with probability from math competitions (its so annoyting when u can never get match your answer with the tests answers, but you keep on trying different ways but none of them works). I have looked at tons of probability and combinatorics books, but my advice is to start up with the easier books such as a stat. text or a detailed discrete math text rather than some Olympiad book, for I had found myself such pressures don't work at all. You can know how to do one problem, but the next one, you'll be stuck again. </p>
<p>For fun, try this probability question:</p>
<p>An engineer arranges 12 poles in a linear fashion. 3 poles are painted blue, 4 are painted green, and 5 are red. What is probability that when he random arranges them in the line, the no red poles will be adjacent to each other?</p>
<p>For fun, try this probability question:</p>
<p>An engineer arranges 12 poles in a linear fashion. 3 poles are painted blue, 4 are painted green, and 5 are red. What is probability that when he random arranges them in the line, the no red poles will be adjacent to each other?
Excluding the five red poles, there are 7 other poles
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there are 8 places to put the red poles
so no. of arrangements of red poles = 8P5
and the no. of arrangement of the 7 poles = 7!/3!4!
therefore, the total no. of arrangements is = 8P5 x 7!/3!4!</p>
<p>the total no. of arrangements is 12!
therefore, the probability is 8P5 x 7!/3!4! / 12! = 0.0005</p>