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CAT 2023 Slot 3 · Quant · Permutations, Combinations and Sets · medium

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

Numerical answer

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

Word MOBILE has 6 distinct letters: consonants M, B, L and vowels O, I, E. Treat the 3 vowels as one block, giving 4 units (M, B, L, [vowel-block]) to arrange: 4! = 24 ways. Within the block, the 3 vowels can be arranged in 3! = 6 ways. Total arrangements = 24×6 = 144.
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Original question written in the CAT 2023 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake