In how many ways can Abby, Bonnie, Chuck, Dennis, Ed and Fred line up at the water fountain so that the two girls, Bonnie and Abby, are not beside each other?

Answer 1

number of ways without restriction is
6! or 720

let's put Abby and Bonnie together
number of ways = 2x5! = 240

(I multiplied 5! by 2 because it could have been Abby-Bonnie or Bonnie-Abby)

So the number of ways they are not together is 720-240 or 480