You win a prize in a charity raffle. The prize, donated by a small hotel chain, is a voucher…

You win a prize in a charity raffle. The prize, donated by a small hotel chain, is a voucher entitling you to a free double room for a weekend at each of the three hotels in the chain, the Xerxes, the York and the Zetland. The room you stay in at each hotel will be picked at random by the hotel manager. The Xerxes has 12 double rooms, 7 of which are en suite. The York has 28 double rooms, 16 of which are en suite. The Zetland has 18 double rooms, of which 13 are en suite. (a) What is the probability that none of the rooms you get is en suite? (b) What is the probability that one of the rooms you get is en suite? (c) What is the probability that two or more of the rooms you get are en suite?