QA – Placement Quizzes | Permutation and Combination | Question 2

What is the number of possible words that can be made using the word “QUIZ” such that the vowels never come together?
(B) 8
(C) 12
(D) 16
(E) 24


Answer: (C)

Explanation: The word “QUIZ” has 4 letters in which “UI” are vowels.
Total number of possible words = 4!
Treating “UI” as a single letter we can make words in 3! ways.
“UI” can be arranged in 2! ways.
Therefore, the number of words can be made using vowels together = 3! * 2! = 12 ways.
Hence, the number of words can be made such that vowels never come together = 24 – 12 = 12 ways.

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