How many words can be formed with the letters of the word $^{'} O M E G A^{'}$ when vowels being never together?

12

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36

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24

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84

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Solution

The correct option is C $84$
OMEGA
Treat the vowels $O, E, A$ as single entity.
Number of ways when vowels are together $3! \times 3! = 36$
Total ways for arranging letters of omega $= 5! = 120$
Words when vowels will not be together $= 120 - 36 = 84$

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