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 there are 5 vowels (A, E, I, O, U) and 3 consonants (Q, T,N)

The numbers of ways in which 5 vowels can be arranged are


………………1


Similarly, the numbers of ways in which 3 consonants can be arranged are 3C3


……………..2


There are two ways in which vowels and consonants can appear together


(AEIOU)(QTN) or (QTN)(AEIOU)


the total number of ways in which vowel and consonant can appear together are:


2 × 5C5 × 3C3


2 × 120 × 6 = 1440


2
1