  In this paper we derived in QCD the BFKL linear, inhomogeneous equation for
the factorial moments of multiplicity distribution($M_k$) from LMM equation. In
particular, the equation for the average multiplicity of the color-singlet
dipoles($N$) turns out to be the homogeneous BFKL while $M_k \propto N^k$ at
small $x$. Second, using the diffusion approximation for the BFKL kernel we
show that the factorial moments are equal to: $M_k=k!N( N-1)^{k-1}$ which leads
to the multiplicity distribution:$ \frac{\sigma_n}{\sigma_{in}}=\frac{1}{N} (
\frac{N\,-\,1}{N})^{n - 1}$. We also suggest a procedure for finding
corrections to this multiplicity distribution which will be useful for
descriptions of the experimental data.
