What is the probability of forming a word from the letters of the word "IMPEACH" such that all vowels come together?

Correct answer: 2/7

Solution

The word IMPEACH has 7 distinct letters, with vowels I, E, A. If all vowels come together, treat them as one block. The number of favorable arrangements is \(5!\times 3!\), and total arrangements are \(7!\), giving probability \(\frac{5!\cdot 3!}{7!}=\frac{2}{7}\).

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