A Cisco router has learned three different routes to the same destination network. An EIGRP route has a composite metric of 20684570, an OSPF route has a metric cost of 852, and a RIPv2 route has a hop count of 4. Based on default administrative distances, which route or routes will be installed in the routing table?

Introduction / Context:
This question evaluates your understanding of how Cisco routers choose between multiple routes to the same destination network when those routes are learned from different routing protocols. It is important to know that before comparing protocol specific metrics such as EIGRP composite cost, OSPF cost, or RIP hop count, the router first uses the concept of administrative distance to determine which routing source is considered the most trustworthy by default.

Given Data / Assumptions:
- One route comes from EIGRP with a composite metric of 20684570.
- One route comes from OSPF with a metric value of 852.
- One route comes from RIPv2 with a hop count metric of 4.
- All three routes describe the same destination network prefix.
- Default Cisco administrative distances are in use: EIGRP internal 90, OSPF 110, RIPv2 120.

Concept / Approach:
Administrative distance represents the trust level of a routing information source. Lower administrative distance values are preferred over higher values. Cisco routers compare administrative distance before comparing metrics within a single protocol. EIGRP internal routes have an administrative distance of 90, OSPF has 110, and RIPv2 has 120 by default. Because 90 is the lowest among these, the EIGRP route will be selected without even considering the detailed metric values. The specific composite, cost, or hop count values only come into play when comparing routes from the same routing protocol.

Step-by-Step Solution:
Step 1: Write down the default administrative distances: EIGRP internal 90, OSPF 110, RIPv2 120.Step 2: Note that all three routes point to the same destination prefix, so administrative distance must be used to pick between protocols.Step 3: Compare the distances. The smallest value among 90, 110, and 120 is 90 for EIGRP.Step 4: Conclude that the EIGRP route is preferred over OSPF and RIPv2 because it has the most trustworthy source by default.Step 5: Recognize that the exact EIGRP composite metric of 20684570, the OSPF cost of 852, and the RIP hop count of 4 are not cross compared because they are from different protocols.

Verification / Alternative check:
A quick verification approach is to remember the common ordering of default administrative distances on Cisco equipment: connected 0, static 1, EIGRP internal 90, IGRP 100, OSPF 110, IS IS 115, RIP 120, and EIGRP external 170. In that sorted list EIGRP internal appears before OSPF and RIPv2, confirming that the EIGRP route is the one that will be installed into the routing table.

Why Other Options Are Wrong:
The option claiming that only the OSPF route will be installed ignores the fact that OSPF has a higher administrative distance than EIGRP. The choice that only the RIPv2 route is installed is incorrect since RIP has the highest distance of the three. Installing all three routes and load balancing would only occur if the routes came from the same protocol and had equal administrative distance and metric values. A combination of OSPF and RIPv2 routes is also invalid when an EIGRP route with a better distance is available.

Common Pitfalls:
A very common mistake is to compare the protocol specific metric values directly, such as 4 hops versus an OSPF cost of 852, which simply does not make sense because they are on different scales. Another pitfall is forgetting the actual default administrative distance values and assuming that newer protocols always win. Memorizing the relative ordering of distances is usually enough to answer many exam questions quickly and accurately.

Final Answer:
Only the EIGRP route will be installed in the routing table because it has the lowest default administrative distance.