In how many ways can the letters of word "EDUCATION" be arranged such that NO two vowels appear together?
Select:  A) 9!  B) 5!*4!  C) 5!*5!  D) 5!*4!*2!  E) 6!*4!
No 2 vowels together = the only arrangement possible will be V C V C V C V C V (with V=vowel, C=consonant). This is true as we have 5 vowels and 4 consonants and any other combination will force us to pair 2 vowels together.   Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 5!*4! ----&gt; 5!*4! is the correct answer.
<result>B</result>
In how many ways can the letters of word "EDUCATION" be arranged such that NO two vowels appear together?