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 12 family members in a row for the picture?  Choose one:
A) 13!
B) 11×10!
C) 10×11!
D) 12!/2!
E) 12!
The number of ways to arrange 12 people is 12!   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 11 units.   The number of ways to arrange 11 units is 11!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 12! - 2*11! = 11!*(12-2) = 10x11!   The answer is 10×11!.
<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 12 family members in a row for the picture?