Suppose there were three events that could be done in any order. Let these events be A, B and C. There are a total of 6 possible ways the events can be performed.

However, this time, there is a restriction. B can only be performed after A. In other words, A must be performed before B can, and ACB is also accepted.

Your task is to find a general formula for X number of events, and Y number of restrictions.

None of the events is mentioned in more than one restriction.

The problem addresses only restricions of "A before B" type.

However other restricions exist; e.g. "A and B are neighbors",

"A is neither first or last ","A and B are never neighbors", etc

As opposed to the first type restriction (halving the number of admissible permutations) these cause other results and therefore should be evaluated each according to its definition.