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...
Question 1 Report
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.
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