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COUNTING TECHNIQUES: PROBABILITY AND STATISTICS

3. The word FACETIOUS is one of the only words in the English language to contain all five vowels in alphabetical order. If these nine letters are arranged randomly, what is the probability that the resultingword also contains the five vowels in order?

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Answer #1

here number of ways to arrange 9 letters =9! =362880

number of ways to arrange letters so that vowels are in order =N(arrange vowels in order and then we have six places for each of 4 consonants between and out of this vowels)=1*6*6*6*6=1296

therefore probability that all 5 vowels are in order =1296/362880 =1/280

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