You take care of n children and to keep them busy, you provide to them (not to every child individually) n toys, randomly selecting from a big box with n blue toys and n red toys. The children don't like red toys. If children get k red toys (for any k), they will return these k toys to you and complain. In this case, you will discard there k toys and you find out another k toys selected uniformly at random from the leftover toys in the big box. If they get red toys again as well as they might complain again, but at this point you just give up and do nothing. Determine the probability that they get all the blue toys in the end?