Q.2. How many words, with or without meaning, can be formed using all the letters
of the word EQUATION at a time so that the vowels and consonants occur together?
In the word EQUATION, we have
vowels = 5(A,E,I,O,U)
consonants = 3(Q,T,N)
Since all the vowels and consonants occur together so (AEIOU) and (QTN) can be assumed as single objects.
Then, permutations of these two objects taken at a time
Corresponding to each of these permutations, there are permutations for vowels and permutations for consonants.
Thus, by multiplication principle, required the number of different words
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