JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Permutations and Combinations

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The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ____.

Answer: 50400

Solution

ASSASSINATION has the six vowels A,A,A,I,I,O and the seven consonants S,S,S,S,N,N,T. Keeping the vowels together as a single block leaves

8

units—the block and the seven consonants—which arrange in

\frac{8 !}{4 ! 2 !}

ways, the

4!

and

2!

removing the repeats of S and N. Within the block the vowels arrange in

\frac{6 !}{3 ! 2 !}

ways. Multiplying,

\frac{8 !}{4 ! 2 !} \times \frac{6 !}{3 ! 2 !} = 840 \times 60

, so the number of such words is

50400

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer

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