Countif formula to match multiple criteria

please see the attached workbook.

on sheet 2 column C, i would like the formula to match the date in column A and the employee number in column B to the date and employee number on sheet 1 AND...
count the amount of times the conditions match the column header.

so for example, in cell C2 on sheet 2, i would like the amount of times employee number 1 on the 17/08/2013 had 1stfloor; bad; fast; and summer listed across a row.
in cell C3, id like the same thing but for employee 2.

columns D,E, and F do not need to be done. i put them in to help give an idea of what im doing.



thank you!!!

i was hoping the formula would contain the words "fast" and "winter" etc.
the reason being that due to very senesitive nature of my work, i just created a simple example workbook but obviously would like to transfer the formula you provide to my real workbook.

is there a way to actually use the words in the formula?

im assuming there is no need for array brackets.

also, because i dont know how many dates there will be in the future, sheet 1 can continue to grow beyond row 46. ive tried replacing $A$2:$A$46 with just A:A but i get a N/A error.
what can i do to fix this

thanks so much

Jeffrey's suggestion is superior to mine, you could just use a much larger number on the range.

=COUNTIFS(Sheet1!$A$2:$A$9999,$A2,
Sheet1!$B$2:$B$9999,$B2,
Sheet1!$C$2:$C$9999,"1stfloor",
Sheet1!$D$2:$D$9999,"bad",
Sheet1!$E$2:$E$9999,"fast",
Sheet1!$F$2:$F$9999,"summer")

perfect.
thanks guys