Question

Denote by SS the set of integers {−44,−43,...,−38−44,−43,...,−38}. Count the number of BIJECTIVE functions φ:S→Sφ:S→S such that φ(x)≠xφ(x)≠x for all x∈S.

Answer 1

Answer:

5039

Step-by-step explanation:

Since a bijective function of a set onto itself is nothing but a permutation of S and  the set  

S={-44, -43, -42, -41, -40, -39, -38}

has 7 elements, there are 7! = 5040 possible bijective functions of S onto itself.

But there is only one such that φ(x) = x

Hence, there are 5040-1 = 5039 bijective functions of S onto itself such that φ(x)≠x.