Calculate the latency $($from first bit sent to last bit received$)$ for the following:

CHAPTER $1$ Foundation

$($a$)10-$Mbps Ethernet with a single store$-$and forward switch in the path and a packet size of $5000$ bits. Assume that each link introduces a propagation delay of $10$ us and that the switch begins retransmitting immediately after it has finished receiving the packet.

$($b$)$ Same as $($a$)$ but with three switches.

$($c$)$ Same as $($a$)$ but assume the switch implements "cut$-$through" switching: it is able to begin retransmitting the packet after the first $200$ bits have been received.