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

Question

Infinity Learn · Accepted Answer

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  $$7C2The$$ 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 $$(21)(14)74=6/49$$.

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

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