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Question
The number of ways of arranging letters of the ‘HAVANA’, so that V and N do not appear together, is ______.
Options
60
80
100
120
MCQ
Fill in the Blanks
Solution
The number of ways of arranging letters of the ‘HAVANA’, so that V and N do not appear together, is 80.
Explanation:
Given word is ‘HAVANA’ (3A, 1H, 1N, 1V)
Total number of ways of arranging the given word
= `(6!)/(3!)`
= 120
Total number of words in which N, V together
= `(5!)/(3!) xx 2!`
= 40
∴ Required number of ways = 120 – 40 = 80
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Permutations - Permutations When Some Objects Are Identical
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