Question 4: You are playing laser tag. The players are a mix of 8 adults and 5 children. The staff tell you to line yourselves up against the wall in order to pick teams. (a) How many ways can you arrange everyone in a line if all children must be separated, that is, no two children may be beside one another? (b) Assume that we allow up to 2 children to line up together, but never 3 or more together. How many ways can everyone be lined up now? Hint: It is easier to place the parents first then arrange the children among them