In a sequence of coin tosses one can keep a record of the number of instances when a tail is immediately followed by a head, a head is immediately followed by a head, etc. We denote these by T H, H H, etc. For example, in the sequence HHTTHHHHTHHTTTT of 15 coin tosses we observe that there are five H H, three H T, two T H and four T T subsequences. How many different sequences of 15 coin tosses will contain exactly two H H, three H T, four T H and five TT subsequences?