Question

The number of ways in which an examiner can assign $30$ marks to $8$ questions, awarding not less than $2$ marks to any question is?

• A. ${}^{21}\mathrm{C}_7$
• B. ${}^{30}\mathrm{C}_{16}$
• C. ${}^{21}\mathrm{C}_{14}$
• D. None of these

Answer 1

The correct option is C

${}^{21}\mathrm{C}_{14}$

The explanation for the correct answer.

Find the number of ways.

There are $8$ which should be at least of $2$ marks.

Therefore total marks of $8$ question $=16$

Now only $14$ marks are left.

We have to distribute $14$ marks among $8$ students.

Here $\mathrm{n}=8,\mathrm{r}=14$

Therefore the number of ways $={}^{\mathrm{n}+\mathrm{r}-1}{\mathrm{C}}_{\mathrm{r}}={}^{8+14-1}{\mathrm{C}}_{14}={}^{21}{\mathrm{C}}_{14}$.

Hence option $\left(c\right)$ is the correct answer.