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Question
In an examination a student has to answer 5 questions, out of 9 questions in which 2 are compulsory. In how many ways a student can answer the questions?
Solution
Total number of questions = 9
Number of questions to be answered = 5
Since 2 questions are compulsory
A student must select 3 questions from dying remaining 7 questions
The number of ways of selecting 3 questions from 7 questions is = 7C3
∴ The number of ways of answering 5 questions = 7C3
= `(7!)/(3!(7 - 3)!)`
= `(7!)/(3! xx 4!)`
= `(7 xx 6 xx 5 xx 4!)/(3! xx 4!)`
= `(7 xx 6 xx 5)/(3!)`
= `(7 xx 6 xx 5)/(3 xx 2 xx 1)`
= 7 × 5
= 35
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