How many ways can 6 people be lined up to get on the bus. If certain 2 people refuse to follow each other how many ways are possible?
+23245 There are 2! = 2 ways to arrange the 2 refuseniks.
There are 4! = 24 ways to arrange the other 4.
Multiplying these together, we get 48 ways.
There are 10 different places to put the refuseniks: (X = refusenik; - = other)
X-X--- -X-X-- --X-X- ---X-X
X--X-- -X--X- --X--X
X---X- -X---X
X----X
10 x 48 = 480 ways.
