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 `2//7` b. `12//49` c. `32//343` d. none of these

Options

A. `2//7`
B. `12//49`
C. `32//343`
D. `6//49`

Answer

D

Explanation

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 `(.^(7)C_(2))(14) = (21) (14)` Thus, the required probability is `(21)(14)//7^(4) = 6//49`.