How many different words can be formed using the letters of the word “EDUCATION‘ such that, All the consonants are always together ?Options6! X 46!2 X 8!6! X 4!
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 46!2 X 8!6! X 4!
Solution
The word "EDUCATION" has 9 letters in total, in which there are 5 consonants (D, C, T, N) and 4 vowels (E, U, A, I, O).
When the question says "all the consonants are always together", we can treat all the consonants as a single letter. So, we have 5 "letters" to arrange: 4 vowels and 1 "consonant group".
The number of ways to arrange these 5 "letters" is 5! (5 factorial).
Within the "consonant group", we have 5 consonants that we can arrange in 5! ways.
So, the total number of words is 5! * 5! = 14400.
Therefore, the correct option is not listed in your options.
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