If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is

The total number of ways in which papers of 4 students can be checked by seven teachers is 7⁴. 

The number of ways of choosing two teachers out of 7 is ${ }^7{C}_2$The number of ways in which they can check four papers is 2⁴. 

But this includes two ways in which all the papers will be checked by a single teacher. 

Therefore, the number of ways in which 4 papers can be checked by exactly two teachers is 2⁴ - 2 = 14. 

Therefore, the number of favorable ways is $\left({ }^7{C}_2\right)\left(14\right)=\left(21\right)\left(14\right)$ 

Thus, the required probability is $\frac{\left(21\right)\left(14\right)}{7^4}=6/49.$