David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 14 family members in a row for the picture?  Choices
A) 12!	B) 13×12!	C) 12×13!	D) 14!/2!	E) 14!
The number of ways to arrange 14 people is 14!   We need to subtract the arrangement when these two people are together.   Let's think of these two people as a single unit so there are 13 units.   The number of ways to arrange 13 units is 13!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 14! - 2*13! = 13!*(14-2) = 12x13!   The answer is 12×13!.
<result>C</result>
David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 14 family members in a row for the picture?