stuck in combinatorics exercice , need of help Bob has :

12 Hats
12 shirts
5 Pants
4 Jackets
3 belts Wearing 1 pair of pants and 1 shirt is OBLIGATORY.
4 out of the 12 Shirts are warm so no jacket has to be with them

5 out of the 12 Shirts Can be worn with a Jacket (not necessarily)

The remaining 3 shirts out of the 12 are light to they MUST be worn with a jacket on (Obligatory)

3 pants out of 5 must be worn with belts on

Finally Wearing a hat is OPTIONAL

in how many Ways can bob get dressed ??

MY ANSWER : Upper body: (4 + 5*5 + 3*4)*13 = 533. Here the 5*5 represents the 5 shirts that can be either (a) with one of the 4 jackets or (b) with no jacket. The final 13 is the 12 hats and no hat.

Lower body: other 2 pants CAN be worn with belts. Hence, 2 + 3*3 = 11.

Finally, 533*11 = 5863.
Lower body: $3\cdot 3 + 2\cdot 4 = 17$ since 3 pants must be worn with one of 3 belts, and the other 2 pants have the extra choice of no belt.
Lower body: $3\cdot 3 + 2\cdot 4 = 17$ since 3 pants must be worn with one of 3 belts, and the other 2 pants have the extra choice of no belt.