Suppose n people are seated at random in a row of n seats Ho

Suppose n people are seated at random in a row of n seats. How many of the n! possible arrangements of people have Ms. Jones and Ms. Smith sitting next to each other?

Solution

(n-1)!*2!

Jones and smith can sit in two ways (Jones , Smith ) or (Smith , Jones). This forms one pair

Hence we have n-1 people remaining which arrrange them selves in (n-1)! ways.