In how many ways can a student choose a progr | vedclass

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(A) There are $9$ courses available,out of which $2$ specific courses are compulsory for every student.Since $2$ courses are already selected,the stud

Vedclass · Accepted Answer

$35$

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(A) There are $9$ courses available,out of which $2$ specific courses are compulsory for every student.Since $2$ courses are already selected,the student needs to choose $5 - 2 = 3$ more courses.The number of remaining courses to choose from is $9 - 2 = 7$.Therefore,the number of ways to choose the remaining courses is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Number of ways $= ^{7}C_{3} = \frac{7!}{3!4!} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} = 35$.

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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