Note    : Whenever you use a formula, please detail in sentences exactly how/why it works for your particular solution (merely plugging values into a formula does not by itself demonstrate understanding). Proving a more general case of the formula(e) is another valid strategy.

Question: 

Use inclusion-exclusion principle together with an appropriate way of counting to find the number of integer solutions to a + b+ c+ d = 15 such that they satisfy 2 < a < 4 and -2