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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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Verified Answer
Out of available nine courses, two are compulsory. Hence, the student is free to select 3 courses out of 7 remaining courses. If $\mathrm{P}$ is the number of ways of selecting 3 courses out of 7 courses, then
$\begin{aligned}
P &=\mathrm{C}(7,3)=\frac{7 !}{3 !(7-3) !}=\frac{7 !}{3 ! 4 !} \\
&=\frac{7 \times 6 \times 5 \times 4 !}{3 \times 2 \times 1 \times 4 !}=7 \times 5=35 \text { ways }
\end{aligned}$
$\begin{aligned}
P &=\mathrm{C}(7,3)=\frac{7 !}{3 !(7-3) !}=\frac{7 !}{3 ! 4 !} \\
&=\frac{7 \times 6 \times 5 \times 4 !}{3 \times 2 \times 1 \times 4 !}=7 \times 5=35 \text { ways }
\end{aligned}$
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