IB Maths AA HL. May 2017 TZ2 P2 Q8 (arrangements).

In a trial examination session a candidate at a school has to take 18 examination papers including the physics paper, the chemistry paper and the biology paper. No two of these three papers may be taken consecutively. There is no restriction on the order in which the other examination papers may be taken. Find the number of different orders in which these 18 examination papers may be taken.