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 13 family members in a row for the picture? Select the correct option:
A) 14!
B) 12×11!
C) 11×12!
D) 13!/2!
E) 13!
The number of ways to arrange 13 people is 13!   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 12 units.   The number of ways to arrange 12 units is 12!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 13! - 2*12! = 12!*(13-2) = 11x12!   The answer is 11×12!.
<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 13 family members in a row for the picture?