In a classroom of 12 students, only 4 passed the physics test. Unhappy with the students’ performance, the teachers forms a group of 6 of the students to provide feedback on the test. If she randomly chooses the 6 students from the class of 12, what is the probability that the group consists of 3 students who passed the test and 3 who did not? But it does not provide correct answer.

My reasoning was \frac{4}{12}*\frac{3}{11}*\frac{2}{10}*\frac{8}{9}*\frac{7}{8}*\frac{6}{7}

I may be wrong but I think its something like this (4c3*8c3)/12c6
basically what i did was select 3 students who passed the test AND out of remaining 8 i selected 3 more divided by the number of ways i can select 6 students out of 12 Hope this helps

Your method is not correct in this situation, because the order of the students is not important. However, the method you’ve used differentiates between, say, the order of the three students being A, B and C, or B, A and C (where the failed students were named A, B, C and D)

The way you have mentioned:
But because we do not care about the order - you need to multiply it with 6!/(3! x 3!) - as there are 6 students in total (3 of each type)

As Greg would explain: ways that make you happy/Total no of possibilities
(4C3 x 8C3)/ 12C3