I have 4 worksheets with the following tables respectively:

Sheet1 Sheet2 Sheet3 Sheet4
A B A B A B A B
1 X 1 Y 1 X 1 X
2 Y 2 Y 2 Z 2 Y
3 Z 3 X 3 Y 3 Z


I'm trying to create a separate summary sheet where the formula cell will
calculate the following from the 4 worksheets:
1) checks if the column A has "1", then check if column B has "X" in same
row of worksheet;
2) if both criteria are met, it counts as 1 in the formula cell.
3) This step will be repeated for every worksheet.

In the case of the above example worksheets, the formula cell will show a
total of 3 (X appearing 3 times for row 1 where A=1). To elaborate further,
if i now want to count how many "Z" appeared in same row with "3" in the
column A - the result would be 2 per example worksheets above.

Can this be done?