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Q.

The number of arrangements of the letters of the word ‘INDEPENDENCE’ in which all the vowels always occur together is 

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a

16800

b

18000

c

14800

d

33600

answer is B.

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Detailed Solution

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Vowels: I, E, E, E, E
Consonants: N N N D D P C
 IEEEE 3N,2D,P,C
 Number of required words =8!3!2!×5!4!=16800

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The number of arrangements of the letters of the word ‘INDEPENDENCE’ in which all the vowels always occur together is