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

None of these

Total number of ways in which 4 papers can be distributed among 7 teachers = 7⁴

Now exactly 2 teachers out of 7 can be chosen in ⁷C₂ ways. And total number of ways in which 4 papers can be given to these 2 teachers (each one getting atleast one) = (2⁴ – 2) = 14

⇒ Total number of ways in which exactly 2 teachers check all four papers = ⁷C₂ . 14 = 21 . 14

⇒ Required probability = $\frac{21.14}{7^4}=\frac{3.2}{7^2}=\frac{6}{49}$