A must be assigned to position A. Now consider four positions of BCDE, four students, E, P, D and E.

B can't be assigned to B. There are three alternative arrangements, CDE.

The remaining students have three students and three places, and there is an arrangement of A(3)(3)=6.

So * * * has 3*6= 18 arrangements.

However, if all the above conditions are not considered, there will be A(5)(5)= 120 arrangement for five students and five posts.

So the probability = 18/ 120=3/20.