A data center consists of 5 servers, S1, . . . , S5. Each server fails independently with probability p during the day. Failed servers are restarted at the end of each day. Give all of the following answers as a function of p - simplify the resulting expressions as far as possible.

a) What is the probability that exactly two servers fail on a given day?

b) A major re-design requires additionally that a server among {S2, S3, S4} must remain operative. What is the probability that the data center fails on a given day (as a function of p)?