Question

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

• A. $2/7$
• B. $12/49$
• C. $32/343$
• D. None of these

Answer 1

Answer: (D)

The total number of ways in which papers of $4$ students can be checked by seven teachers is $7^4$. The number of ways of choosing two teachers out of $7$ is ${}^7{C}_2$. The number of ways in which they can check four papers is $2^4$. 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 $2^4-2=14$. Therefore, the number of favorable ways is $\left({}^7{C}_2\right)(14)=(21)(14)$. Thus, the required probability is $(21)(14)/7^4=6/49$.