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 15 family members in a row for the picture? Choose the correct choice from the following options
A) 15!
B) 14×13!
C) 13×14!
D) 14!/2!
E) 13!
The number of ways to arrange 15 people is 15!   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 14 units.   The number of ways to arrange 14 units is 14!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 15! - 2*14! = 14!*(15-2) = 13x14!   The answer is 13×14!.
<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 15 family members in a row for the picture?