DMC has an input alphabet X $=\{1,2,3,4\},$ output alphabet V $=\{1,2,3,4,5\}$ and transition probabilities given as p$($yl$)[0\mathrm{.}350\mathrm{.}150\mathrm{.}150\mathrm{.}350\mathrm{.}150\mathrm{.}35000\mathrm{.}150\mathrm{.}350\mathrm{.}3500\mathrm{.}3500\mathrm{.}1500\mathrm{.}15001($a$)$ Find an expression for capacity and the capacity$-$achieving distribution for this channel. $($b$)$ What is the capacity when the input sequence x$$ is subject to the con$-$ straint that probability of $4$th input symbol being used is less than or equal to $1/5?$