Who will check your paper?

There are 4 students attending a test and 7 teachers available for checking the tests. Each student's test is checked by exactly one of these teachers, with each teacher being equally likely to be the one who checks the test. The probability that all the 4 papers are checked by exactly 3 teachers is equal to \(k\left (\frac{6}{7} \right )^{2}\). Find \(k\).

Details: Each paper is checked by only 1 teacher.

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