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?

Question

Philoid · Accepted Answer

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