JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Permutations and Combinations

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The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ______.

Answer: 576

Solution

VOWELS has the six distinct letters V, O, W, E, L, S, with four consonants (V, W, L, S) and two vowels (O, E). All six letters give

6! = 720

arrangements. Treating the four consonants as a single block, that block together with the two vowels gives

3!

orders, and the consonants inside the block

4!

orders, i.e.

3! \cdot 4! = 144

arrangements with all consonants together. Those in which the consonants are not all together number

720 - 144 = 576

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Integer answer

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