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N1, N2 and N3 are possible combination of select k out of 6 items for 1st box, l out of 6-k items for 2nd box and 6-k-l out of 6-k-l items for 3rd box. Note that N3 is always 1.
Nall = 0;
for k = 0:6
N1 = nchoosek(6,k);
for l = 0:6-k
N2 = nchoosek(6-k,l);
N3 = nchoosek(6-k-l,6-k-l);
Nall = Nall + N1*N2*N3;
end
end
The answer is:
>> Nall
Nall =
729
