wonder if someone can help me out?

Please look at this information below:
Each individual has a some kind of a skill set.
Each individual is scheduled certain day (light brown table)
I would like to build a formula which would allow me to find out how many
particular skillsets I have in each day.
This is what would be for one single cell.
=IF(AND(IF(Z15=1,1,0),IF(W15=1,1,0)),1,"")
This is a logical value(TRUE equals 1). for each person I would need a cell
to have this formula and sum it up for all of them.
This task using this method would require if there was 15 people , 15 cells
times 6 days, times 10 skills, just to sum it up to one number.
Imagine 157 people!!!
As you see I need some serious help from you guys.
thank you very much.
Robert