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. $\frac{2}{7}$
• B. $\frac{32}{343}$
• C. $\frac{12}{49}$
• D. None of these

Answer 1

Answer: (D)

None of these

Total number of ways in which $4$ papers cane be distributed among $7$ teachers $=7^4$ ways

Now exactly $2$ teachers out of $7$ can be chosen in ${}^7{C}_2$ ways.

And total number of ways in which $4$ papers can be given to these $2$ teachers $($ each one getting atleast one$)=(2^4-2)=14$

$\Rightarrow$ Total number of ways in which exactly $2$ teachers check all four papers ${=}^7{C}_2\times 14=21\times 14$

$\Rightarrow$ Required probability $=\frac{21.14}{7^4}=\frac{3.2}{7^2}=\frac{6}{49}$