If you need to make several searches and
you want to save typing,
enter this formula below Countx:
=SUMPRODUCT((Type=TypeX R)*(ID=IDx R)*(Group=GroupX R))
Formula is in R1C1 style.
Arrange your search data this way and name it:
TypeX IDx GroupX Countx
A BOX017 S1 1
B BOX017 S1 2