Question 144

In how many different ways can the letters of the word CORPORATION be arranged in such a way that the vowels always come together ?


The letter of the word CORPORATION can be classified into
vowels: O,O,A,I,O
Consonants: C,R,P,R,T,N
If vowels are to be together, lets consider them as one entity, we also have 6 consonants, 2 of which are similar, Thus in total we have 7 entities, 2 of which are similar
So possible arrangements are 7!/2! = 5040/2 = 2520
Now there will also be internal arrangement among the vowels, this will happen in 5!/3! ways = 20
So the total possible ways = 2520*20 = 50400.
Thus, option 5 is the answer.

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