multiple criteria in count function

I need some assistance in getting this formula right. Here is my objective
WORKSHEET (WS) 1
A.............B.............C.......D.......E
1XLast N.......First N......#
2XLast N.......First N......#
3YLast N.......First N......#
4ZLast N.......First N......#

WORKSHEET (WS) 2
A.............B.............C.......D.......E
1 # #
2XLast N.......First N.....count instances from WS1 that = WORKSHEET2A1and XLast Name and XFirst Name
3YLast N.......First N.....same as above but for YLast Name and YFirst Name
4ZLast N.......First N.....same as above but for ZLast Name and ZFirst Name

I need the formula for the Worksheet 2 C cells to look for the WS2XLast Name, WS2XFirst Name with a value of WS2A1 in the C Column of WS1 and count them.

I hope this makes sense. Every if statement and Vlookup try doesn't seem to work.

I'm not 100% clear, but I believe this is what you are looking for:

This would be in cell C2 of sheet2 if I understand correctly:
=SUMPRODUCT((Sheet1!$A$1:$A$10=Sheet2!A2)*(Sheet1!$B$1:$B$10=Sheet2!B2)*(Sheet1!$C$1:$C$10=Sheet2!$A$1)*(1))

Cell C3:
=SUMPRODUCT((Sheet1!$A$1:$A$10=Sheet2!A3)*(Sheet1!$B$1:$B$10=Sheet2!B3)*(Sheet1!$C$1:$C$10=Sheet2!$A$1)*(1))

Cell C4:
=SUMPRODUCT((Sheet1!$A$1:$A$10=Sheet2!A4)*(Sheet1!$B$1:$B$10=Sheet2!B4)*(Sheet1!$C$1:$C$10=Sheet2!$A$1)*(1))

Based on this information:
X-Last X-First 1
X-Last X-First 2
Y-Last Y-First 3
Z-Last Z-First 5
X-Last X-First 1
X-Last X-First 2
Y-Last Y-First 3
Z-Last Z-First 1
X-Last X-First 1
X-Last X-First 2

The values returned were 3, 0, and 1 respectively.

X-Last X-First 1 MATCH
X-Last X-First 2
Y-Last Y-First 3
Z-Last Z-First 5
X-Last X-First 1 MATCH
X-Last X-First 2
Y-Last Y-First 3
Z-Last Z-First 1 MATCH
X-Last X-First 1 MATCH
X-Last X-First 2

That seems to be working!