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In how many ways can a student choose a programme of courses if courses are available and specific courses are compulsory for every student?
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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.
Thus, the required number of ways of choosing the programme
$$\Rightarrow ^{7}C_3 =\displaystyle \dfrac {7!}{3!\, 4!}$$
$$=\displaystyle \frac {7\times 6\times 5}{3\times 2\times 1 }$$
Therefore, every student has to choose $$3$$ courses out of the remaining $$7$$ courses.
This can be chosen in $$^7C_3$$ ways.
Thus, the required number of ways of choosing the programme
$$\Rightarrow ^{7}C_3 =\displaystyle \dfrac {7!}{3!\, 4!}$$
$$=\displaystyle \frac {7\times 6\times 5}{3\times 2\times 1 }$$
$$=35$$
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| Question Text | In how many ways can a student choose a programme of courses if courses are available and specific courses are compulsory for every student? |
| Answer Type | Text solution:1 |
| Upvotes | 150 |
