# Practice GMAT Problem Solving Question

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A test maker is to design a probability test from a list of 21 questions. The 21 questions are classified into three categories: hard, intermediate and easy. If there are 7 questions in each category and the test maker is to select two questions from each category, how many different combinations of questions can the test maker put on the test?

Correct Answer:

**A**- In this problem order is not important. For example, the selection of question 1, 8 and 21 is the same as the selection of question 21, 8 and 1. Since order is unimportant, the combination formula applies.
- The formula for a combination is:

_{n}C_{r}= n!/((n-r)!r!)

where n is the total number of selections available and r is the number of items to be selected. - Since the test maker must select a total of six questions and two questions from each category, the combination formula is used. Since there are 3 categories and two questions will be selected for each of the 3 categories, total number of combinations is:

=_{7}C_{2}*_{7}C_{2}*_{7}C_{2} - There are a total of (
_{7}C_{2})^{3}combinations.

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