Final answer:
To provide a subnet with 72 nodes, the proper CIDR notation would be a /25 subnet mask, as it allows for 128 total addresses, which is the smallest subnet size that can accommodate 74 addresses (72 usable addresses plus one network and one broadcast address).
Step-by-step explanation:
To allocate an appropriate number of IP addresses for a subnet with 72 nodes, you will need to ensure that there are at least 72 usable IP addresses. Each IPv4 subnet has two addresses that cannot be used for nodes: one for the network address and one for the broadcast address. Since we need 72 usable addresses, we have to consider these two additional addresses, bringing our total to 74.
The closest number that can accommodate this requirement is 128, since that is the smallest power of 2 that is greater than 74. The subnet that can provide 128 addresses is a /25 subnet, as it has 128 total addresses (including the network and broadcast addresses). Thus, the correct CIDR notation would be a subnet mask of /25, which indicates that 25 of the 32 bits are used for the network portion of the address, leaving 7 bits for host addresses (2^7=128 total addresses).