We will be constructing strings from the alphabet $W,x,Y,Z$ in this

problem. Call such strings WXYZ strings. How many WXYZ strings

of length $8$ contain

$($a$)$ exactly $3$ W$\text{'}$s$?$

$($b$)$ at most $3W\text{'}$s$?$

$($c$)$ exactly $3$ W$\text{'}$s and exactly $2$ Z$\text{'}$s$?$

$($d$)$ are palindromic $($i$.$e$.$ read the same forward and backward, for

example XXWZZWXX$)?$