How many 7-letter words can be formed using all the alphabets of the word SIMILAR given the condition that all the vowels are not together.

Answer Choices

Correct answer marked below

1800

2160

Correct

4320

4680

None of these

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Explanation

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Official Explanation

Official

7-letter words using all 7 letters of SIMILAR =

\frac{7!}{2!}

(because I repeats twice)

7-letter words using all 7 letters such that all vowels are together:

Tie the vowels together into 1 group - IIA which can be arranged in 3 different ways (IIA, IAI, AII).

Now we need to arrange 5 different letters/groups - S, M, L, R, and the vowel group, which can be done in

5!

ways.…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.