## mathmath333 one year ago Counting problem

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{In how many ways can a student choose a programme } \hspace{.33em}\\~\\ & \normalsize \text{of 5 courses if 9 courses are available and 2 specific } \hspace{.33em}\\~\\ & \normalsize \text{courses are compulsory for every student.} \hspace{.33em}\\~\\ \end{align}}

2. phi

I assume order does not matter. we just want a list of 5 courses.

3. mathmath333

order doesn't matter.

4. phi

you have to choose the 2 required courses. that leaves 7 from which to pick 3 7 choose 3 right ?

5. mathmath333

yes

6. phi

and that is 35

7. mathmath333

u did $$^{7}C_{3}$$ ,but what about the remaining $$2$$ courses

8. phi

we could be pedantic and say 2C2 * 7C3

9. mathmath333

ok 2C2=1

10. mathmath333

11. phi

yes. Make sense?

12. mathmath333

yes thnks

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