Answer
$4.00\times10^{17}$ photons per second.
Work Step by Step
Find the photon energy.
$$E=hf=h\frac{c}{\lambda}$$
$$E=\frac{1.24\times10^{-6}eV\cdot m}{10.6\times10^{-6}m }= 0.117eV$$
We know the power of the laser beam is 7.50mW, so 7.50mJ per second is delivered. This is $4.69\times10^{16}$ eV. The number of photons delivered per second can then be calculated.
$$N=\frac{4.69\times10^{16}eV/s}{0.117eV /photon}=4.00\times10^{17} photons/s$$
