MATLAB: List combinations and count how many it appears

list

I have 2 matrices, W and Y. Using both as references, I want to list the different combinations and count how many times it appears from Y. Only count Y if the correponsing W value is >0.
W =[ 25
     0
     0
    28
     0
     0
    25
     0
     0
    25
     0
     0
    15
    14
     0
     0
    25
     0
     0];
 
Y =[ 1     2     0     0
     1     3     2     0
     1     4     3     2
     1     3     0     0
     1     2     3     0
     1     4     3     0
     1     4     0     0
     1     3     4     0
     1     2     3     4
     2     3     0     0
     2     1     3     0
     2     1     4     3
     2     1     4     0
     2     3     4     0
     2     1     3     4
     2     3     1     4
     3     4     0     0
     3     1     4     0
     3     2     1     4];
 
Zlist =
[12;
13;
14;
23;
24;
34;]
Add 2 1 to 1 2; 3 1 to 1 3; 4 1 to 1 4; 3 2 to 2 3; 4 3 to 3 4 and 4 2 to 24
Also, for Y with more > 2 numbers in the row like [2 1 4], it will have a combinations of 2 1, 1 4, 2 4 while [2 3 4] has 2 3, 3 4 and 2 4. 
Zlistcount =
[2;
1;
2;
2;
2;
2;]

Best Answer

YY = Y(W~=0,:);
n = sum(YY>0,2);
k = factorial(n)./factorial(n-2)/2;
ie = cumsum(k);
ib = ie - k + 1;
zc = zeros(ie(end),2);
for ii = 1:numel(ib)
    zc(ib(ii):ie(ii),:) = sort(nchoosek(YY(ii,YY(ii,:)>0),2),2); 
end
[i1,i2,v] = find(accumarray(zc,1));
Zlistcount = [i1,i2,v];
and without loop (as in Dpb's answer):
YY = Y(W~=0,:);
zc = sort(cell2mat(arrayfun(@(x)nchoosek(YY(x,YY(x,:)>0),2),...
                                    (1:size(YY,1))','un',0)),2);
[i1,i2,v] = find(accumarray(zc,1));
Zlistcount = [i1,i2,v];
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