Child Welfare Academy Competency Exam Practice 2026 - Free Competency Exam Practice Questions and Study Guide

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If a case has 3 clients, how many relations must be created according to the formula number of clients in a case times (clients in a case minus 1)?

This uses a simple counting idea: when every client in a case has a relation with every other client, and the order of the relation matters, you multiply the number of clients by one less than that number. With three clients, each client can connect to the other two, giving 2 relations per client. Multiply by the total number of clients: 3 × 2 = 6.

So there are six distinct directed relations: from each client to the other two (A to B, A to C, B to A, B to C, C to A, C to B). If you were just counting undirected pairs, you’d get 3, but this formula counts ordered connections, which is why the result is six.