In how many ways can a student choose (n-2) courses out of n courses if 2 courses are compulsory (n \gt 4)?
- A. (n-3)(n-4)
- B. (n-1)(n-2)
- C. (n-3)(n-4)/2
- D. (n-2)(n-3)/2 ✓
Correct Answer: D. (n-2)(n-3)/2
Explanation
The student needs to choose n-2 courses in total. Since 2 courses are compulsory, they are already pre-selected. The student must now choose the remaining (n-2) - 2 = n-4 courses from the remaining n-2 available non-compulsory courses. The number of ways is \binom{n-2}{n-4} = \binom{n-2}{2} = \frac{(n-2)(n-3)}{2}.
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