The accounts of Pullman Plumbers, Inc. are being audited by an independent accounting firm. The company currently has 100 active accounts, of which 50 are current accounts, 35 are past due 60 or more days, and 15 accounts are delinquent. The accounting firm will randomly choose five different accounts in their auditing procedure.

(a) What is the probability that none of the accounts chosen will be delinquent accounts?

(b) What is the probability that at most one of the accounts chosen will be delinquent?

(c) What is the probability that there will be three current, one past due, and one delinquent accounts chosen?

(d) What are the expected numbers of the various types of accounts that will be chosen?