detailed solution

Correct option is B

The total number of ways in which papers of 4 students can be checked by seven teacher is $7^4$

The number of ways of choosing two teachers out of 7 is ${}^7\mathrm{C}_2$. The no. of ways in which they can check four papers is $2^4$. But this includes two ways in which all the papers will be checked by a single teacher.

= The number of ways in which 4 papers can be checked by exactly two teachers is $2^4-2=14$

$\therefore$ The number of favourable ways $=\left({}^7\mathrm{C}_2\right)\left(14\right)=\left(21\right)\left(14\right)$

$\therefore$ Required probability $=\frac{\left(21\right)\left(14\right)}{7^4}=\frac{6}{49}$