How many ways can we arrange the word “examination” such that no vowels come together?
I am trying to do this question from a high school textbook. The answer given is 1058400, but I can't get this answer. Here's what I've tried so far: There's 11!/(2^3) arrangements without any restrictions If the two As are adjacent, then there's 10!/(2^2) arrangements (you can swap the As, but since they are repeated there's no need to) Then you can have AE, AI, EI adjacent. In each case this is (10!*2!)/(2^3), as the two vowels can be swapped around, but the As are repeated. Subtracting these cases from the number of arrangements without any restrictions gives 1360800, which is not the answer.
Discussion :: Permutation and Combination - General Questions (Q.No.13)
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