Find the number of possible different arrangements of the letters of the word OPTICAL such that the vowels would always be together.

Correct answer:

n =  720

Step-by-step explanation:

OIA PTCL  n1=(4+1)!=120 n2=3!=6  n=n1 n2=120 6=720

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the word OPTICAL has three vowels and 4 consonants. Since all the three vowels are to be together, mark as one symbol X This with the 4 consonants become 5 which can be permuted in 5! = 120 ways. The three vowels in X can be permuted among themselves in 3! = 6 ways.

The total number of arrangements of the letters of the word OPTICAL so that all the vowels are always together is 120 x 6 = 720.

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