Question
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Answer: Option D
In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters = $$\frac{{7!}}{{2!}}$$ = 2520
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in $$\frac{{5!}}{{3!}}$$ = 20 ways
∴ Required number of ways = (2520 x 20) = 50400
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In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters = $$\frac{{7!}}{{2!}}$$ = 2520
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in $$\frac{{5!}}{{3!}}$$ = 20 ways
∴ Required number of ways = (2520 x 20) = 50400
Was this answer helpful ?
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