A network administrator wants to use the same subnet mask for three subnetworks with given numbers of devices. Which subnet mask would be appropriate?

The appropriate subnet mask for the scenario involves ensuring that the subnet can accommodate all the devices required across the three subnetworks. The choice of subnet mask directly affects how many individual hosts can be assigned IP addresses in each subnet.

The mask of 255.255.255.240 allows for 16 IP addresses (2^4 = 16, since there are 4 bits for the host part) within a subnet, but it only has 14 usable addresses (subtracting 2 for the network and broadcast addresses). This means that if each of the three subnetworks requires a number of IP addresses that is less than or equal to 14, this mask is suitable. Thus, it is a good fit for situations where you have subnetworks with limited demands, such as a handful of devices per subnet.

In contrast, other subnet masks offer either too few or too many addresses that wouldn't efficiently use the IP space. The option of 255.255.255.0 allows for 256 addresses (254 usable), which could lead to waste if the devices needed are relatively small. 255.255.255.128 provides 126 usable addresses in a single subnet, far exceeding the needs for smaller subnetworks. Lastly, the 255.