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?

Answers (1)
S seema garhwal

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 =^2P_2=2!=2

Corresponding to each of these permutations, there are 5! permutations for vowels and 3! permutations for consonants.

Thus, by multiplication principle, required the number of different words = 2\times 5!\times 3!=2\times 120\times 6=1440