Question

If the papers of 4 students can be checked by any one of the seven teachers , then the probability that all the four papers are checked by exactly two teachers is

• A. $\frac{6}{49}$
• B. $\frac{2}{7}$
• C. $\frac{32}{343}$
• D. $\frac{2}{343}$

Answer 1

The correct option is A $\frac{6}{49}$

Select $2$ teachers from the $7$ teachers in ${}_2^{7}C=21$ ways.
The $2$ teachers can check the $4$ papers in $2^4-2=16-2=14$ ways (we remove $2$ because it corresponds to the cases where all papers are checked by a single teacher).
Therefore, the probability = $\frac{21\ast 14}{7^4}=\frac{6}{49}$