Question

In an objective paper, there are two sections of $10$ questions each. For "section $1$", each question has $5$ options and only one option is correct and "section $2$" has $4$ options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in "section $1$" is $1$ and in "section $2$" is $3.$
(There is no negative marking)
If a canidate in total attempts $4$ questions all by guessing, then the probability of scoring $10$ marks is

• A. $\frac{1}{15}\times (\frac{1}{15}{)}^3$
• B. $\frac{4}{15}\times (\frac{1}{15}{)}^3$
• C. $\frac{1}{15}\times (\frac{14}{15}{)}^3$
• D. None of these

Answer 1

The correct option is D None of these

Scoring $10$ marks from four questions can be done in $3+3+3+1=10$ ways so as to answer $3$ questions from section $2$ and $1$ question from section $1$ correctly. Hence, the recquired probability is
$=\frac{1}{5}\times (\frac{1}{15}{)}^3$