Question
In how many ways can the letters of the word "EXAMPLE"
be arranged, and what is the probability that all the vowels in these arrangements always appear together?Solution
ATQ;
Word: EXAMPLE Letters: 7 total (E appears twice) Total arrangements: = 7! / 2! = 5040 / 2 = 2520 Vowels together (E, E, A → 1 block): Remaining letters: X, M, P, L → total blocks = 5 - Ways to arrange 5 blocks = 5! = 120 - Ways to arrange vowels (E, E, A) = 3! / 2! = 3 - Total favorable = 120 × 3 = 360 Probability (vowels together): = 360 / 2520 = 1 / 7
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