Counting the number of rows that contains specific numbers in specific cells

Question

I'm trying to find a way to count the number of rows in a matrix that contains specific elements in specific cells.

For example, suppose I have the following matrix

Data={{1,1,1,1},{1,1,0,1},{1,0,0,1},{0,1,0,0},{1,0,0,0},{1,0,1,0},{1,1,1,1},{0,1,0,0}}

What I want to find is the number of rows that is consistent with the following list:

list1={1,Null,Null,1}

So, in the data, {{1,1,1,1},{1,1,0,1},{1,0,0,1},{1,1,1,1}} is consistent with the list1, so the output should be 4.

Another example is if list2={1,1,1,1}, then the output should be 2. If list3={1,Null,Null,Null}, then we should have 6 as there are 6 rows starting with 1.

How can this situation be efficiently programmed? The length of each row is the same in the data and I have a very large size of the zero-one matrix.

Answer 1

list1={1,Null,Null,1}
sel = Map[If[# === Null, __, #] &, list1];
Cases[Data, sel]

list2 = {1, 1, 1, 1};
sel = Map[If[# === Null, __, #] &, list2]
Cases[Data, sel]

list3 = {1, Null, Null, Null};
sel = Map[If[# === Null, __, #] &, list3]
Cases[Data, sel]

Answer 2

data = {{1, 1, 1, 1}, {1, 1, 0, 1}, {1, 0, 0, 1}, {0, 1, 0, 0}, {1, 0,0, 0}, {1, 0, 1, 0}, {1, 1, 1, 1}, {0, 1, 0, 0}};

Cases[data, {1, _, _, 1}] // Length
(* 4 *)

Cases[data, {1, 1, 1, 1}] // Length
(* 2 *)

Cases[data, {1, _, _, _}] // Length
(* 6 *)