In how many ways can the letters of word ABDUCTION be arranged such that NO two vowels appear together?
Choose the most appropriate option: A) 9! B) 5!*4! C) 4!*5! D) 5!*4!*2! E) 6!*4!
No 2 vowels together = the only arrangement possible will be C V C V C V C V C (with V=vowel, C=consonant). This is true as we have 4 vowels and 5 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 = 4!*5! ----&gt; 4!*5! is the correct answer.
<result>C</result>
In how many ways can the letters of word ABDUCTION be arranged such that NO two vowels appear together?