A psychology class is comprised of 4 female and 6 male students. If the instructor of the class randomly chooses 6 students from the class for an oral exam, what is the probability that 2 female students and 4 male students will be selected? Round your answer to 3 decimal places

P = 4/10(F) * 3/9(F) * 6/8(M) * 5/7(M) * 4/6(M) * 3/5(M) = ?

Try them in reverse order to see if you get the same answer.

P = 6/10(M) * 5/9(M)....

To calculate the probability, we need to find the total number of possible combinations and the number of favorable combinations.

The total number of possible combinations can be calculated using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of students in the class, and r is the number of students to be chosen for the oral exam.

In this case, there are 10 students in total, and 6 students are to be chosen for the oral exam:

C(10, 6) = 10! / (6! * (10 - 6)! )
= 10! / (6! * 4!)
= (10 * 9 * 8 * 7 * 6!) / (6! * 4!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 10 * 9 * 8 * 7 / 4
= 10 * 9 * 2 * 7
= 1,260

So, there are 1,260 possible combinations.

Now, let's find the number of favorable combinations. We need to select 2 female students out of 4 and 4 male students out of 6. We can calculate this using another combination formula:

C(n1, r1) * C(n2, r2) = (n1! / (r1! * (n1 - r1)!) ) * (n2! / (r2! * (n2 - r2)!) )

where n1 is the total number of female students, r1 is the number of female students to be chosen, n2 is the total number of male students, and r2 is the number of male students to be chosen.

In this case, we have:

C(4, 2) * C(6, 4) = (4! / (2! * (4 - 2)! ) ) * (6! / (4! * (6 - 4)! ) )
= (4! / (2! * 2!) ) * (6! / (4! * 2!) )
= (4 * 3 * 2!) * (6 * 5 * 4 * 3 * 2!) / (4 * 2!) )
= (4 * 6 * 5 * 4) / 2
= 480

So, there are 480 favorable combinations.

Finally, we can calculate the probability:

P(2 female and 4 male) = favorable combinations / total combinations
= 480 / 1260
= 0.381

Therefore, the probability that 2 female students and 4 male students will be selected for the oral exam is approximately 0.381.