In how many ways can the letter of the word “REALITY” be arranged such that no two vowels are together ?*1) 6!-4!2) 13203) 3!4!4) 1440
Question
In how many ways can the letter of the word “REALITY” be arranged such that no two vowels are together?
Options:
6! - 4!13203! 4!1440
Solution
The word "REALITY" has 7 letters in total, out of which 3 are vowels (E, A, I) and 4 are consonants (R, L, T, Y).
Step 1: Arrange the consonants first. There are 4 consonants which can be arranged in 4! = 24 ways.
Step 2: Now, we have 5 places (represented by *) where we can place the vowels such that no two vowels are together: * R * L * T * Y *
Step 3: We have 3 vowels which can be arranged in these 5 places in 5P3 = 60 ways.
So, the total number of ways the letters of the word "REALITY" can be arranged such that no two vowels are together is 24 * 60 = 1440 ways.
So, the correct answer is 4) 1440.
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