python - Looking for an algorithm to count the number of possible patterns -


i need in constructing algorithm solve following problem:

a 5x5 table can filled values ​​0 , 1 each line , each column of table consists of 2 ones , 3 zeros. how many solutions exist?

if want provide code, can freely use preferred language. use r, matlab , python.

i tried convert table vector: 

unique(perms([ones(1,10),zeros(1,15)]), 'rows')

then, each row, form 5x5 table , check if row sums , col sums equal 2. above command generated error: ??? maximum variable size allowed program exceeded.

here python expression bute forces matrices 2 1s per row:

from itertools import * print len(filter(   lambda candidate: all(imap(     lambda index: sum(imap(lambda _: _[index], candidate)) == 2,     xrange(5)   )),   product(set(permutations([0,0,0,1,1])), repeat=5) ))

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