Answer
${\bf 2\times 10^7}\;\rm photon$
Work Step by Step
We know that the probability density is given by
$$\text{Prob}( \text{in } \delta x \text{ at } x)=P(x)\delta x=\dfrac{N }{N_{tot}}$$
where $N_{tot}$ is the total number of photons, and $N$ is the number of photons detected at position $\delta x$.
Hence,
$$N=N_{tot}P(x)\delta x$$
Plug the known;
$$N=(1\times 10^{10}) (20)(0.1\times 10^{-3})$$
$$N =\color{red}{\bf 2\times 10^7}\;\rm photon$$
