How many different words can be formed using the letters of the word “EDUCATION‘ such that, All the consonants are always together ?Options6! X 4!6!6! X 42 X 8!
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 4!6!6! X 42 X 8!
Solution
The word "EDUCATION" has 9 letters in total, including 5 vowels (E, U, A, I, O) and 4 consonants (D, C, T, N).
When the question states that all consonants must be together, we can think of all the consonants (D, C, T, N) as a single letter. So, we now have 6 "letters" to arrange: E, U, A, I, O, and "DCTN".
These 6 "letters" can be arranged in 6! (6 factorial) ways.
However, within the "DCTN" group, the 4 consonants can also be arranged amongst themselves. This can be done in 4! (4 factorial) ways.
So, the total number of ways the letters in the word "EDUCATION" can be arranged such that all consonants are always together is 6! * 4!.
Therefore, the correct option is 6! X 4!.
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