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					 In how many ways can the letters of the word 'Director' be arranged so that the three vowels are never together ?
 
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- 1800
 - 18000
 - 16000
 - 1600
 
 
Correct Option: B
Total number of letters = 8 
Number of vowels  = 3 and r  occurs twice. 
Total number of arrangements when  there is no restriction  = 8!/2!
When three vowels are together, regarding them as one letter, we have only  5 + 1 = 6 letters 
These six letters can be arranged in 6!/2! ways, since r occurs twice. 
But the three vowels can be arranged among  themselves in 3! ways. 
Hence number of arrangement when the three vowels are together = 6! /(2 !x 3!)
∴ Required number = 8!/2! - {6! / (2! x 3!)} = 18,000