Column A has names say Row1 - Muthu, Row 2 - Karthi Row 3 - Sundaram
Column B has period say Row1 - Quarter, Row 2 - Quarter, Row 3 - Half
Column C has results say Row 1 - Pass, Row 2 - Pass, Row 3- Fail,

I need a formula to find out how many pass & fail are in Quarter, Half, Final

Hi,

You have four possibilities, so my recommendation is :
cell F1 type Pass
cell G1 type Fail
cell E2 type Quarter
cell E3 type Half

Then in cell F2 type following formula :
=SUMPRODUCT(--($B$1:$B$3=$E2),--($C$1:$C$3=F$1))

Then copy this formula to cell G2, F3 and G3

HTH