In how many ways can the letters of the word MANIFOLD be arranged so that the vowels are separated ?	Choose one:  A) 14400  B) 36000  C) 18000  D) 24000  E) 22200
We have 3 vowels: AIO and 5 consonants: MNFLD.   Consider the following case: *M*N*F*L*D* If we place vowels in any 3 empty slots (*) then all vowels will be separated by at least one consonant:   The # of ways to choose 3 empty slots out of 6 for 3 vowels = C36=20C63=20;   The # of ways to arrange the vowels: 3! (or instead of these two steps we could use P36)P63);   The # of ways to arrange MNFLD = 5!.   Total = 20*3!*5! = 14,400.   14400nswer: 14400
<result>A</result>
In how many ways can the letters of the word MANIFOLD be arranged so that the vowels are separated ?