did you mean
let | A | = n and | B | = m
1) Howmany functions from A to A which are bi-jective
2) Howmany functions from A to B which are bi-jective
3) Howmany functions from A to B which are bi-jective
4) Howmany functions from A to B which are bi-jective
note that 2,3 and 4 are equal.
for all this questions n! is the answer, but note that m should be equal to n for 2,3,4 due to it is necessary condition for bijection