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In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together?

Correct Answer: 3600

Explanation:

Given word is THERAPY.


Number of letters in the given word = 7


These 7 letters can be arranged in 7! ways.


Number of vowels in the given word = 2 (E, A)


The number of ways of arrangement in which vowels come together is 6! x 2! ways


 


Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.


 


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