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CAT 2024 Slot 2 · Quant · Permutations, Combinations and Sets · medium

How many distinct arrangements of the letters of the word 'ORANGE' are possible if all the vowels (O, A, E) must always come together?

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How many distinct arrangements of the letters of the word 'ORANGE' are possible if all the vowels (O, A, E) must always come together?
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Answer: 144

Treat the block of 3 vowels (O,A,E) as a single unit. Along with the 3 consonants (R,N,G), we now arrange 4 units: 4! = 24 ways. Within the vowel block, the 3 vowels can be arranged in 3! = 6 ways. Total = 24 × 6 = 144.
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Original question written in the CAT 2024 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake