It is well$-$known that cyber$-$attacks have increased not only in South Africa, but worldwide. The Cybersecurity Hub, South Africa's National Computer Security Incident Response Team $($CSIRT$)$ who strives to make cyberspace an environment where all residents of South Africa can safely communicate, socialise, and transact in confidence, recommends that online accounts passwords are changed quarterly. They found that only $80\%$ of South Africans change passwords on online accounts quarterly, as recommended.

a$)$ how many different samples can be drawn where $5$ out of the possible $16$ change their passwords quaterly.

b$)$ if a dandom sample of $5$ residents is drawn, calculate the probability that only the first and last resident in the sample will change their passwords quaterly.