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?
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?
There are $9$ courses available out of which, $2$ specific courses are compulsory for every student.
Therefore, every student has to choose $3$ courses out of the remaining $7$ courses. This can be chosen in $^{7} C_{3}$ ways.
Thus, required number of ways of choosing the programme
$=\,^{7} C_{3}=\frac{7 !}{3 ! 4 !}=\frac{7 \times 6 \times 5 \times 4 !}{3 \times 2 \times 1 \times 4 !}=35$
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