First slide

Theorems of probability

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

Moderate

A

$\frac{2}{7}$
B

$\frac{12}{49}$
C

$\frac{32}{343}$
D

None of these

Solution

The total number of ways in which papers of 4 students can be checked by seven teachers is 7⁴.
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 2⁴.
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 2⁴ - 2 = 14.
Therefore, the number of favorable ways is $(^{7} C_{2}) (14) = (21) (14)$
Thus, the required probability is $\frac{(21) (14)}{7^{4}} = 6 / 49 .$

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