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 11 family members in a row for the picture?	Answers.
A) 12!
B) 10×9!
C) 9×10!
D) 11!/2!
E) 11!
The number of ways to arrange 11 people is 11!   We need to subtract the arrangements when these two people are together.   Let's think of these two people as a single unit so there are 10 units.   The number of ways to arrange 10 units is 10!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 11! - 2*10! = 10!*(11-2) = 9x10!   The answer is 9×10!.
<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 11 family members in a row for the picture?