Explanation:
* DHCP scopes: 3
* DHCP relays: 2
In a Windows Server Hybrid Core Infrastructure, managing IP address assignment across multiple physical or virtual segments requires a combination of DHCP scopes and Relay Agents. A DHCP scope is a required administrative grouping of IP addresses for computers on a specific subnet that use the DHCP service. Since the network consists of three distinct IPv4 subnets (two client VLANs and one datacenter VLAN), you must create a minimum of three scopes to ensure each subnet is managed and provided with appropriate configuration options, such as default gateways and DNS servers specific to their segment. Even if the DHCP server resides in the datacenter VLAN, the scope for that subnet allows for the management of any other devices or future clients in that segment.
Regarding the distribution of these addresses, DHCP utilizes broadcast traffic (DHCPDISCOVER), which is restricted to the local Layer 2 broadcast domain (the VLAN). To allow the DHCP server in the datacenter to receive requests from the two remote client VLANs, a DHCP Relay Agent (or IP Helper) must be configured on the gateway or a local server within those segments. The minimum number of relays required is two, corresponding to the two client VLANs that do not host the DHCP server. The datacenter VLAN does not require a relay because the DHCP server is directly connected to that broadcast domain and can listen for local requests natively. This configuration adheres to the design principles of centralized DHCP management in a segmented enterprise environment.