$1.$ Three different processors P$1,$ P$2,$ P$3$ executing the same set of instructions. P$1$ has a $3$ GHz clock rate and a CPI of $1\mathrm{.}5.$ P$2$ has $2$ GHz clock rate and CPI of $1\mathrm{.}2.$ P$3$ has $4$ GHz and CPI of $2\mathrm{.}4.$

a$.[5$ pts$]$ Which processor has the best performance for that set of instruction? Which is worst?

b$.[5$ pts$]$ Assume the CPI for these three processors remains the same as specified to run a program of $1$ billion instructions, how much time does each processors take to run this program?