Current Attempt in Progress

A coil C of $N=116$ turns is placed around a long solenoid $S$ of radius $R=5\mathrm{.}14cm$ and $n=217$ turns per meter, as in the figure below. $($a$)$ What is the mutual inductance for the coil$-$solenoid combination? $($b$)$ Does it depend on any of these three: the shape, size, or possible lack of close packing of the coil?

$($a$)$ Number

Units

$($b$)$