Using drop down boxes and needing them to check each other before counting the amount

Hello,
I am having trouble figuring out the exact formula to count how many times a letter(s) appears in certain columns using a drop down box and counting them depending on what is selected in the boxes then placing them in a certain area. I have attached a sample sheet and provided a detailed description of exactly what i am trying to accomplish. If someone could please help me out i would greatly appreciate it. Thanks in advance.