See the formula on page 399 in:
http://stat.gamma.rug.nl/Snijders_Psychometrika1991_Enumeration_Simulation.pdf
EDIT For a more general setup see:
MR2600999 (2011e:05005) Barvinok, Alexander(1-MI) On the number of matrices and a random matrix with prescribed row and column sums and 0–1 entries. (English summary) Adv. Math. 224 (2010), no. 1, 316–339.