The coupon collector problem characterizes the expected number of days that it takes to get n coupons if one receives one of these coupons at random every day in the mail. This number is approximately n ln n. Use this fact to compare the number of TCP connections that are initiated in a sequential port scan, going from port 1 to 65535, directed at some host, to the expected number that are

requested in a random port scan, which requests a random port each time (uniformly and independently) until it has probed all of the ports.

What will be an ideal response?

A sequential port scan will initiate 65,535 TCP connections, whereas a ran
dom port scan will initiate an expected 65, 535 ln 65, 535, which is about 72, 6805. This is
approximately 11 times more TCP requests.