How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that no two consonants are together.

Number of letters = (all distinct)
Number of vowels = 5 (e, i, o, u, a)
Number of consonants = 3 (q, t, n)
Arrange the vowels in a row by leaving one place between every two vowels.
Number of permutations of arrranging vowels                    ...(i)
    V        V        V       V       V     
 1             2                 3           4            5            6
Number of places for the consonants, so that no two of them are together = 6
Number of consonants = 3
                           n = 6,  r = 3
Number of permutations of arranging consonants:
                                                      ...(ii)
Hence, using (i) and (ii), the number of words formed so that no two consonants are together, using fundamental principle of counting
                             = 120 x 120 = 14400