To calculate the total number of possible passwords if the length is exactly $8$ characters, we need to multiply the number of choices for each character. Since the password policy requires at least one uppercase letter, one digit, and one special character, we can assume that the password contains exactly one of each, and the remaining five characters are lowercase letters. Therefore, the number of choices for each character is:$1$st character: $26($uppercase letters$)2$nd character: $10($digits$)3$rd character: $11($special characters$)4$th to $8$th character: $26($lowercase letters$)$The total number of possible passwords is then:$26*10*11*26^5=1,976,156,160$To calculate the entropy of passwords adhering to this policy, we need to use the formula:E $=$ log$2($RL$)$where E is the entropy, R is the number of possible characters in the password, and L is the length of the password$12.$ Since the password policy requires at least one uppercase letter, one digit, and one special character, we can assume that the password contains exactly one of each, and the remaining five characters are lowercase letters. Therefore, the number of possible characters in the password is:R $=26+10+11+26=73$The length of the password is:L $=8$The entropy of the password is then:E $=$ log$2(73^8)=43\mathrm{.}3$ bitsThe significance of entropy and variance in relation to the security implications of the systems password policy is that they measure how difficult it is for an attacker to guess or crack the password using brute$-$force attacks. The higher the entropy and variance, the more secure the password is$.$ Entropy