Final answer:
To enable outbound internet connectivity for virtual machines in an Azure subnet using a pool of public IP addresses, an Azure Load Balancer and Network Security Groups should be included in the design.
Step-by-step explanation:
To design network connectivity for a subnet in an Azure virtual network that allows 30 virtual machines to establish outbound connections to the internet using the same pool of four public IP addresses while preventing inbound connections, the inclusion of the following elements is required:
Azure Load Balancer: You'll need an Azure Load Balancer to manage outbound connections from the virtual machines through a set of public IP addresses. This allows the VMs to share the four public IPs for outbound traffic, providing a way to hide the internal IP addresses and distribute the load.
Network Security Groups (NSGs): NSGs should be configured to enforce inbound and outbound access policies. By setting appropriate rules, you can prevent inbound connections to the virtual machines while allowing outbound traffic to the internet.
A Virtual Network Gateway is not required in this scenario since it is typically used for hybrid networking connections, such as a site-to-site or point-to-site VPN. Similarly, an Azure Application Gateway isn't necessary unless layer 7 load balancing is required, which is not implied in the question.