Solve the following problem using the principle of inclusion and exclusion: Suppose there are only three types of faculties in a college: the newly recruited lab professors (LP), the assistant professors (AP), and the teaching professors (TP). Each professor has to be at least in one of these three categories. And the total number of professors in the school is 1230. Suppose that the following is given: The number of faculties who are LP is 320. The number of faculties who are AP is 750. The number of faculties who are TP is 460. The number of faculties who are both LP and AP is 20. The total of faculties who are both LP and TP is 130. The total of faculties who are both AP and TP is 190. What is the total number of faculties who fit into all 3 categories?

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.