Fun problem

Fun problem - Fun problem: We have the "word"...

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Fun problem: We have the “word” HOWMEOWCOW. If we were to arrange the letters at random, what is the probability that we get the 3 O’S before we get the C? Let us use our total probability formula. There are 10 spaces total. Let us examine each of the ten cases (where we position c). If C is in spot 1, we cannot have our event. If C is in spot 2, we cannot have our event. If C is in spot 3, we cannot have our event. If C is in spot 4, we CAN HAVE OUR EVENT. Now we need to worry about how many ways this is possible. The first part of this statement is how many ways can we arrange the O’s before the C. The 2 nd part of the statement is how many ways can we arrange the remaining 6 letters after already placing the 3 O’s. Given C is in the forth spot, there are 3 3    ways to arrange the 3 O’s before the C. Next there are 6 3,1,1,1 ways to arrange the other 6 letters. What about if C is in spot 5?
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Fun problem - Fun problem: We have the "word"...

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