I was going through PnC questions and I came across this problem.

Four balls numbered $1,2,3,4$ are to be placed into five boxes numbered $1,2,3,4,5$ such that exactly one box remains empty and no ball goes to its own numbered box. The no. of ways is?

I worked out the problem in the following way.

Case 1: box 5 is not selected and thus total derangements $d_4=9$

Case 2: Any one of 4 boxes say box 1 is not selected $ C(4,1)$

case 2(a) ball 1 goes to box 5 then total derangements $d_3=2$

Case 2(b) ball 1 goes to either of other two boxes say box 2

Case 2(b)(i) ball 2 goes to 5 then $d_2=1$

Case 2(b)(ii) ball 2 doesn’t go to box 5 then also $d_2=1$

Thus, total number of ways $=9+C(4,1){2+2*2}=33$

But none of the answer matches. Please help me identify error in the reasoning.