The diagram lists various types of operating systems (LNX, W2K, WSP), databases (ORA, MSQ, SQL), and application servers (JBS, WSP) supported by the application under test. To test all possible combinations of these types, we need to multiply the number of options in each category. In this case, we have:

3 options for operating systems

3 options for databases

2 options for application servers

Therefore, we have 3 x 3 x 2 = 18 possible combinations to test.

However, if we look closely at the diagram, we can see that some combinations are not valid or feasible because they are not connected by lines. For example, we cannot test LNX with WSP as an application server because there is no line between them. Similarly, we cannot test W2K with JBS as an application server because there is no line between them. Therefore, we need to exclude these invalid combinations from our calculation.

If we count only the valid combinations that are connected by lines in the diagram, we get:

5 combinations for LNX (LNX-ORA-JBS, LNX-ORA-WSP, LNX-MSQ-JBS, LNX-MSQ-WSP, LNX-SQL-JBS)

5 combinations for W2K (W2K-ORA-WSP, W2K-MSQ-WSP, W2K-SQL-WSP)

5 combinations for WSP (WSP-ORA-JBS, WSP-ORA-WSP, WSP-MSQ-JBS, WSP-MSQ-WSP)

Therefore, we have 5 + 5 + 5 = 15 valid combinations to test.

You can find more information about testing combinations in Software Testing Foundations: A Study Guide for the Certified Tester Exam, Chapter 4, Section 4.22.