Probability Practice Test 1

The paper of each student can go to any of the nine professors.
As there are 5 students, there are 9 × 9 × 9 × 9 × 9 = 95
ways in which the papers can be checked by the professors.
Now, number of ways of selecting two professors =9C2
The five papers can be checked by the two professors in 25 ways, but this will contain two ways in which the papers are checked by just one professor.
∴ The number of ways in which 5 answer sheets are checked by exactly two professors =9C2×(25−2)
Number of ways in which each paper can be checked by a professor = 2
∴ Number of ways such that five papers can be checked by those 2 professors =9C2×(25−2)
Probability =

9C2×(25−2)

95

=

40

2187