Bernoulli flips a coin \(15\) times and writes down the sequence of heads (H) and tails (T) that he gets. He notices that he has 5 instances of consecutive TH, 4 instances of consecutive HT, 3 instances of consecutive HH and 2 instances of consecutive TT. How many different sequences could he have written down?

**Details and assumptions**

As an explicit example, if the sequence was HTTHHT, then there are 1 instance of consecutive TH, 2 instances of consecutive HT, 1 instance of consecutive HH and 1 instance of consecutive TT.

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