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