Discrete Math Denote by S the set of integers 10 9 4 Count

Discrete Math

Denote by S the set of integers {-10, -9, ..., -4}. Count the number of BIJECTIVE functions phi:S rightarrow S such that phi(x) notequalto x for all x epsilon S.

Solution

Since there are 7 elements in the set S i.e.

S = {-10,-9,-8,-7,-6,-5,-4}

The number of bijective mappings from S->S is equal to (number of elements)! = 7! = 5040 mappings

Since we don\'t want phi(x) = x, as the mapping which is only possible if all the elements are mapped with themselves, so removing that mapping

Number of mappings = 5040-1 = 5039 mappings