$(4$ points$)$ Consider the eight$-$point decimation$-$in$-$time $($DIT$)$ flow graph in the following figure.

$($a$)(1$ point$)$ What if the gain of the "signal path" that goes from $x[7]$ to $x(2)?$

$($b$)(1$ point$)$ How many paths lead from the input to a given output sample? Is this true for every output sample?

$($c$)(2$ point$)$ Compute $x(3)$ using the operations dictated by this flow graph.