SAT Example (the Mathematics Section)
작성자
CLI 아카데미
작성일
2018-03-02 12:40
조회
1186
Math: Student-Produced Response questions
Correct Answer: 15
Explanation>
There are 6 courses offered; let us refer to them as 1, 2, 3, 4, 5, and 6. One way to find the number of combinations is to list all possible pairings. They are 1-2, 1-3, 1-4, 1-5, 1-6, 2-3, 2-4, 2-5, 2-6, 3-4, 3-5, 3-6, 4-5, 4-6, and 5-6. There are 15 combinations. Note that 1-2 and 2-1 represent the same combination.
You could also notice that there are 5 pairings that start with course 1 and 4 additional pairings that start with course 2, and so forth. The total number of combinations is 5+4+3+2+1 = 15.
You could also solve the problem by noting that the total number of permutations (that is, the number of different ways 2 of 6 courses could be selected) is 6 for the first course selected times 5 for the second course selected, or 6*5 = 30. To find the number of combinations, you must divide the number of permutations by the number of arrangements. For each pair of courses A-B selected, the arrangement B-A is also possible. Therefore, there are 2 arrangements. So, the number of combinations is 30 2 =15.
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