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In how many ways can a student choose a ...

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

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Since, 2 subjects are compulsory out of 9 subjects, so the student can choose 3 subjects out of remaining 7 subjects. So, total ways `= .^(7)C_(3)`.
`= (7!)/(3!4!) = (7 xx 6xx 5 xx 4!)/(3 xx 2xx 1 xx 4!) = 35`.
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