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Question
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
Solution
Given that question number 1 and 2 are compulsory
∴ The remaining questions are 5 – 2 = 3
Total number of questions to be attempted = 4 questions 1 and 2 are compulsory
So only 2 questions are to be done out of 3 questions
Therefore number of ways = 3C2
= 3C3–2
= 3 ......`[∴ ""^nC_r = ""^nC_(n - r)]`
Hence, the required number of ways = 3.
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