What is the probability that on a math test 5 out of 30 students got an A all three got an A on the test if three students are chosen at random without replacement?

The correct answer is option 1/406.
To find the probability of 3 students got an A on a test, multiple the probabilities of the 3 students.

Probability of the first student = 5/30 = 1/6
Probability of the second student = 4/29
Probability of the third student = 3/28
Probability that the 3 students got an A on the test
= (prob. of student 1) * (prob. of student 2) * (prob. of student 3)
= (5/30) * (4/29) * (3/28)
= 60/24360
= 1/406
Hope this helps.

1. 1/406

First, find the probability of picking an A student (5/30 or 1/6), then find the probability of the second A student (4/29) and finally the third A student (3/28). Multiply the probabilities together and reduce to get: 1/406