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Question
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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Solution
If two courses are compulsory, then remaining courses = 9 – 2 = 7
Ways to choose 3 courses out of 7 courses = 7C3
Thus, required number of ways of choosing the programme
= 7C3
= `(7!)/(3!4!)`
= `(7 xx 6 xx 5 xx 4!)/(3 xx 2 xx 1 xx 4!)`
= 35
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