Answer
$9.53\times10^{-21}\,J/K$
Work Step by Step
Number of ways $W=B^{N}=1000^{100}=(10^{3})^{100}=10^{300}$
$S=k\ln W$ where the Boltzmann constant $k=1.38\times10^{-23}\,J/K$
Then $S=(1.38\times10^{-23}\,J/K)\times \ln (10^{300})$
$=9.53\times10^{-21}\,J/K$
