How many different words can be formed using the letters of the word “EDUCATION‘ such that, All the consonants are always together ?Options6! X 42 X 8!6! X 4!6!
Question
How many different words can be formed using the letters of the word “EDUCATION‘ such that, All the consonants are always together ?Options6! X 42 X 8!6! X 4!6!
Solution
The word "EDUCATION" has 9 letters in total, in which there are 5 vowels (E, U, A, I, O) and 4 consonants (D, C, T, N).
When the question says "all the consonants are always together", we can treat these 4 consonants as a single letter. So, we have 6 "letters" to arrange: 5 vowels and 1 "consonant group" (D, C, T, N).
The number of ways to arrange these 6 "letters" is 6!.
However, within the "consonant group", we can arrange the 4 consonants in 4! ways.
So, the total number of different words is 6! * 4!, which is one of the options given. So, the correct answer is 6! X 4!.
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