Question 26

# The answer sheets of 5 engineering students can be checked by any one of 9 professors. What is the probability that all the 5 answer sheets are checked by exactly 2 professors?

Solution

Each of the 5 papers can be checked by any of the 9 professors and thus the total number of way = 9$$^5$$
Selecting exactly 2 of the 9 professors can be done in $$^9C_2$$ way = 36
They can correct the 5 papers in 2$$^5$$ - 2(all the 5 papers checked by the same professor) = 30  ways.
Thus, the total number of ways = 36*30
Hence, the required probability = $$\dfrac{36*30}{9^5}$$ = $$\dfrac{40}{2187}$$
Hence, option B is the correct answer.