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

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(B) Out of the available $9$ courses,$2$ are compulsory. Since the student must choose a total of $5$ courses and $2$ are already fixed,the student ne

Vedclass · Accepted Answer

$35$

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(B) Out of the available $9$ courses,$2$ are compulsory. Since the student must choose a total of $5$ courses and $2$ are already fixed,the student needs to select the remaining $5 - 2 = 3$ courses from the remaining $9 - 2 = 7$ available courses. The number of ways to select $3$ courses out of $7$ is given by the combination formula $C(n, r) = \frac{n!}{r!(n-r)!}$. Here,$n = 7$ and $r = 3$. $C(7, 3) = \frac{7!}{3!(7-3)!} = \frac{7!}{3!4!} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} = 35$. Therefore,there are $35$ ways to choose the programme.

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

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