$5.[20$ points$]$ Consider a genetic algorithm using binary representation with strings of length $5.$ Assume that the initial population $($generation $0)$ was as follows: Individual Genotype Fitness $1100012021110010300011540111015$ Assume also that a standard generational GA $($using $1-$point crossover and bit mutation$)$ is used with mutation probability pm $=0\mathrm{.}01$ and crossover probability pc $=1\mathrm{.}0.($a$)$ Calculate a lower bound for the expected number of representatives of schema $1****$ in generation $1.($b$)$ Calculate a lower bound for the expected number of representatives of schema $0**1*$ in generation $1.$