A test consists of 12 questions out of which candidates are to answer 10. If the first 6 are compulsory, in how many ways can each candidate select her ques...

A test consists of 12 questions out of which candidates are to answer 10. If the first 6 are compulsory, in how many ways can each candidate select her questions?

Answer Details

Out of the 12 questions, the first 6 are compulsory and each candidate must answer them. Therefore, the candidate has to choose 4 questions out of the remaining 6 questions to answer. The number of ways to choose 4 questions out of 6 is given by the formula for combinations: \[\binom{6}{4} = \frac{6!}{4!2!} = \frac{6\times 5}{2\times 1} = 15\] Therefore, each candidate can select her questions in 15 ways. Hence, the answer is 15.