Problem

How many different possible tests can be made from a test bank of 18 questions if the test consists of 2 questions? (Ignore the order of questions.)
It is possible to make different tests.

Answer

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Answer

Final Answer: The number of different possible tests that can be made from a test bank of 18 questions if the test consists of 2 questions is \(\boxed{153}\).

Steps

Step 1 :This problem is about combinations. We are choosing 2 questions out of 18, and the order in which we choose the questions does not matter. The formula for combinations is: \[C(n, k) = \frac{n!}{k!(n-k)!}\] where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 2 :In this case, n = 18 (the total number of questions in the test bank) and k = 2 (the number of questions on the test).

Step 3 :Substituting the values into the formula, we get \[C(18, 2) = \frac{18!}{2!(18-2)!}\]

Step 4 :Solving the above expression, we find that the number of combinations is 153.

Step 5 :Final Answer: The number of different possible tests that can be made from a test bank of 18 questions if the test consists of 2 questions is \(\boxed{153}\).

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