Question

If 9 students write an examination, and if there are 9 teachers available, for the correction of their papers

Answer 1

then each teacher get one paper for correction

Answer 2

The correct question is: If nine students write an examination, and if there are nine teachers available for the correction of their papers, then the probability that all the nine papers are checked by exactly two teachers is _____.

The correct answer is $4.74e-5.$

Given:

Number of students = 9

Number of teachers = 9

To Find:

Using the given data, we have to find the probability that all the nine papers are checked by exactly two teachers.

Solution:

The total number of ways in which papers of 9 students can be checked by 9 teachers = $9^{9}.$

The number of ways of choosing two teachers out of 9 = $^9C_{2} .$

The number of ways in which they can check 9 papers = $2^{9}.$

This also includes the two ways in which all the papers will be checked by a single teacher.

Therefore, the number of ways in which 9 papers can be checked by exactly two teachers = $2^{9} - 2 = 510.$

∴ The number of favorable ways = $^9C_{2}$ × $510$

$= 36$ × $510 = 18,360.$

Therefore, the required probability = $\frac{18360}{9^{9} }$

$= \frac{18360}{387,420,489} = 4.74e-5.$

Hence, the probability that all the nine papers are checked by exactly two teachers is $4.74e-5.$

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