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Question

In how many different ways can the letters of the word “INCORPORATION” be arranged so that the vowels comes together?

A 608400 Correct Answer Incorrect Answer
B 604800 Correct Answer Incorrect Answer
C 648000 Correct Answer Incorrect Answer
D 600840 Correct Answer Incorrect Answer
E 604080 Correct Answer Incorrect Answer

Solution

In the word “INCORPORATION”, we treat the vowels IOOAIO as one letter Thus, we have, NCRPRTN (IOOAIO) This has 8(7+1) letters of which R and N occurs 2 times and the rest are different Number of ways arranging these letters = 8!/(2! ×2!) = 10080 Now, 6 vowels in which O occurs 3 times and I occurs 2 times, can be arranged in 6!/(3! ×2!) = 60 ∴ Required number of ways = 10080 × 60 = 604800

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