SILK-ROAD 2012 Problem 2

In each cell of the table $4 \times 4$ , in which the lines are labeled with numbers $1,2,3,4$ , and columns with letters $a,b,c,d$ , one number is written: $0$ or $1$ . Such a table is called valid if there are exactly two units in each of its rows and in each column. Determine the number of valid tables.