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 7C2. 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  7C2(14)=(21)(14). Thus, the required probability is 21×1474