Question

if the papers of 4 students can be checked by any of the 7 teachers,the show that the probability that all the 4 papers are checked by exactly 2 teachers is 6/49

Answer 1

Conditions

if the papers of 4 students can be checked by any of the 7 teachers, the show that the probability that all the 4 papers are checked by exactly 2 teachers is 6/49

Solution

The probability of this event is the rate for all favorable outcomes (the amount of ways in which we can take fixed 2 teachers from 7) to all possible outcomes (the amount of ways in which we can take any of 7 teachers four times).

For $1^{\text{st}}$ paper we can take a teacher in 7 different ways.

For $2^{\text{nd}}$ – in 6 ways (excluding the $1^{\text{st}}$ chosen teacher)

For $3^{\text{rd}}$ – in 2 ways (first or second teacher)

For $4^{\text{th}}$ – in 2 ways (first or second teacher)

That’s why the probability is:

$$P = \frac{7 - 7 - 2 - 2}{7 - 7 - 7 - 7} = \frac{4}{49}$$

Answer: 4/49, not 6/49