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Question
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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Solution
We are given that 2 courses are compulsory out of the 9 available courses,
Thus, a student can choose 3 courses out of the remaining 7 courses.
Number of ways =\[{}^7 C_3 = \frac{7!}{3! 4!} = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4!} = 35\]
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