  In this paper we found the multiplicity distribution of the produced gluons
in deep inelastic scattering at large $z=\ln\LbQ^2_s/Q^2\Rb\,\,\gg\,\,1$ where
$ Q_s $ is the saturation momentum and $Q^2$ is the photon virtuality. It turns
out that this distribution at large $n > \bar{n}$ almost reproduces the KNO
scaling behaviour with the average number of gluons $ \bar{n} \propto \exp\Lb
z^2/2 \kappa\Rb$, where $\kappa = 4.88 $ in the leading order of perturbative
QCD. TheKNO function $\Psi\Lb \frac{n}{\bar{n}}\Rb = \exp\Lb -\,n/\bar{n}\Rb$.
For $n < \bar{n}$ we found that $\sigma_n \propto\Big( z - \sqrt{2
\,\kappa\,\ln (n-1)}\Big)/(n-1)$. Such small $n$ determine the value of entropy
of produced gluons $S_E = 0.3\, z^2/(2\,\kappa)$ at large $z$. The factor $0.3$
stems from the non-perturbative corrections that provide the correct behaviour
of the saturation momentum at large $b$.
