A container contains 20 lollies of 3 types (5 black, 5 white and 10 clear). Ben Bob and Peter decides to choose 5 lollies each, Ben would only choose the lollies that has an opposite colour to what peter chooses ( i.e. Ben would only choose white if Peter chooses black and vice versa ) unless peter chooses a clear lolly. Bob will not choose a colour similar to peter (i.e. Bob will not choose dark if Peter chooses light and vice versa) unless Peter chose a clear coloured lolly. Peter could only choose a maximum of 3 lollies each from the available type. What is the probability that none of each type of the lollies that Peter, Ben and Bob choose will run out?