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(B) The total number of ways to assign $4$ papers to $7$ teachers is $7^4 = 2401$.To find the number of ways such that exactly $2$ teachers check the

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(B) The total number of ways to assign $4$ papers to $7$ teachers is $7^4 = 2401$.To find the number of ways such that exactly $2$ teachers check the papers,we first select $2$ teachers out of $7$,which can be done in $^7C_2$ ways.Each of the $4$ papers can be checked by either of these $2$ teachers,giving $2^4$ total assignments. However,we must exclude the cases where all papers are checked by only $1$ teacher (i.e.,all $4$ by the first teacher or all $4$ by the second teacher). Thus,the number of ways is $2^4 - 2 = 14$.The number of favourable outcomes is $^7C_2 	imes (2^4 - 2) = 21 	imes 14 = 294$.The probability is $P = \frac{294}{2401} = \frac{6}{49}$.

If the papers of $4$ students can be checked by any one of $7$ teachers,then the probability that all the $4$ papers are checked by exactly $2$ teachers is (in $/49$)

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