Help please, this is more of a theoretical question.

Can you use and + or statements within an array formula.

if I have 3 columns a,b,&c and in these colums I have a list of
integers < 10.

If i wanted to answer the question
Count the incidents where A=1, B=2 AND C=1 OR 2 OR 3
I named the columns a_ b_ and c_ for the sake of ease.


I particularly need to know if I can use an array formula or
sumproduct

My guess of
=SUMPRODUCT((a_=1)*(AND(b_=2,OR(c_=1,c_=2,c_=3)))* 1)

did not work with an exapmle that had 1 sollution

nor did
=SUM(IF(a_=1,IF(AND(b_=2,OR(c_=1,c_=2,c_=3)),1,0), 0))


I think I may have a basic thing wrong but just can not see what it
is.

I know I can solve this a different way but I want to know how to do
it this way.

Thanks in advance for your usual collective help.

Matthew