Of the female students at Barkely University, 5/6 are on the honor rol

We can let the number of students = 120.

Thus, 3/5 x 120 = 72 are female, and 120 - 72 = 48.

So 72 x 5/6 = 60 female students are on the honor roll, and 48 x 2/3 = 32 male students are on the honor roll.

Thus, (60 + 32)/120 = 92/120 = 46/60 = 23/30 are on the honor roll.

Alternate Solution:

Since 3/5 of all students are female, we see that 5/6 x 3/5 = 3/6 = 1/2 of the total students on the honor roll are females. Similarly, since 2/5 of all students are male, we see that 2/3 x 2/5 = 4/15 of the total students on the honor roll are males. Thus, the fraction of all students on the honor roll is:

1/2 + 4/15 = 15/30 + 8/30 = 23/30 of all students are on the honor roll.

Answer: C