Quantitative Reasoning

Permutation & Combination

Medium

In how many different ways, can the letters of words OPTICAL be arranged so that the vowels are never together?

720

1440

4320

5040

✅ Correct Option: 3

OPTICAL has $7$ distinct letters, so total arrangements $= 7! = 5040$ .

Vowels O, I, A are $3$ ; treat them as one block with the $4$ consonants, giving $5!$ arrangements and $3!$ internal orders: $120 \times 6 = 720$ arrangements with vowels together.

Vowels never together $= 5040 - 720 = 4320$ .

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Solution

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