In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?  Choose the correct choice from the following answers:
A) 29P7
B) 29C7
C) 28P7
D) 28C7
E) None
Solution:   First let us consider the 28 unoccupied seats.   They create 29 slots- one on the left of each seat and one on the right of the last one.   We can place the 7 friends in any of these 29 slots i.e. 29P7 ways.   29P7nswer 29P7
<result>A</result>
In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?