Question: A communication system consists of 13 antennas arranged in a line. The system functions as long as no two nonfunctioning antennas are next to each other. Suppose five antennas stop functioning.
(a) How many different arrangements of the five nonfunctioning antennas result in the system being functional? (Hint. This question and the next are related to Example).
(b) If the arrangement of the five nonfunctioning antennas is equally likely, what is the probability the system is functioning?
Example: (a) How many binary sequences of length 10 with exactly four 1's that are not consecutive can be formed?
(b) If a binary sequence of length 10 having four 1's is selected at random, what is the probability that the four 1's are nonconsecutive?