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 equal to

$\frac{6}{49}$

Total ways in which papers can be checked is equal to 7⁴. Now two teachers who have to check all the papers can be selected in ⁷C₂ ways and papers can be checked by them in (2⁴ − 2) favourable ways.

Thus, required probability

$=\frac{{ }^7 C_2 . \left(2^4-2\right)}{7^4}=\frac{6}{49}$