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    Question

    A word consists of 9 letters 5 consonants and 4 vowels.

    Three letters are chosen at random. What is the probability that more than one vowel will be selected.
    A 17/42 Correct Answer Incorrect Answer
    B 23/42 Correct Answer Incorrect Answer
    C 11/42 Correct Answer Incorrect Answer
    D 13/47 Correct Answer Incorrect Answer

    Solution

    Given Data: 9 letters: 5 consonants, 4 vowels. Choosing 3 letters randomly. Find probability of selecting more than one vowel (i.e., 2 vowels + 1 consonant or 3 vowels). Find Total Ways to Pick Any 3 Letters Total ways to choose 3 letters from 9: (9/3) = 84 Find Favorable Cases Case 1: 2 vowels, 1 consonant Case 2: 3 vowels

    Total favorable cases = 30+4 = 34 Find Probability 34/84 = 17/42

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