In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?Choices:- 721 720 711 620
Question
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?Choices:- 721 720 711 620
Solution
To solve this problem, we first consider the three vowels (O, I, A) in the word 'OPTICAL' as a single letter. So, we have 5 letters (P, T, C, L, and the combined vowels). These 5 letters can be arranged in 5! (5 factorial) ways, which equals 120.
Next, the 3 vowels can be arranged among themselves in 3! (3 factorial) ways, which equals 6.
So, the total number of ways the letters in 'OPTICAL' can be arranged such that the vowels always come together is 5! * 3! = 120 * 6 = 720.
Therefore, the correct answer is 720.
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