In how many different ways can the letters of the word "CORPORATION" be arranged in such a way that no two vowels are together?
Options:
A) 6!/2!∗C57∗5!3!	B) 4!/2!∗C57∗5!3!	C) 6!/2!∗C57∗6!3!	D) 3!/2!∗C57∗5!3!	E) 12!/2!∗C57∗5!3!
Step 1: Separate consonants with 7 empty slots *C*R*P*R*T*N*.   Step 2: 6 consonants CRPRTN can be arranged in 6!/2! ways (6 letters with two R's);   Step 3: we have 5 vowels OOAIO. Choose 5 slots out of 7 for them (this way no two vowels will be together): C57   Step 4: 5 vowels in their slots can be arranged in 5!/3! ways (5 letters with three O's).   Total = 6!/2!∗C57∗5!3!   6!/2!∗C57∗5!3!nswer: 6!/2!∗C57∗5!3!
<result>A</result>
In how many different ways can the letters of the word "CORPORATION" be arranged in such a way that no two vowels are together?