Do I need a program?

Say you have two columns, A & B.

Each cell in column A consists of an identical drop-down menu of four possible choices. Each cell in B is a random number.

I want to sum the cells in B according to what the user selects from the drop down in column A.

If A1=A2="BILL", I want the sheet to add B1 and B2.

IF A1=A3="BILL", and A2=A4=TOM, I want the sheet to sum B1 and B3, then sum A2 and A4.

So, conceptually, I guess column A acts as a group identifier, and I want to sum B by group.

Can this be done?