In a high school debating team consisting of 2 freshmen,

[BTGmoderatorLU]

In a high school debating team consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability that the students selected will consist one freshman and one sophomore?

A. 1/16
B. 1/8
C. 1/7
D. 1/6
E. 1/4

The OA is D.

I solve this PS question of the following way,

f =2 , s=2 , j=2 and sn=2
total =8 students
2 are to be selected from 8 such that each is different.

total no. of ways to select 2 from 8= 8C2= 28
number of ways 2 are same = 4 (f,s,j,sn )
28-4=24

selecting 1 freshman from 2, and 1 sophomore from 2 = (2C1 x 2C1)/24= 4/24
=1/6.

Please, can anyone explain another way to solve this question? Thanks in advance.

[GMATGuruNY]

In a high school debating team consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability that the students selected will consist one freshman and one sophomore?

A. 1/16
B. 1/8
C. 1/7
D. 1/6
E. 1/4

Two of the four grades must be selected to represent the team at the championship.
Because each grade on the debate team offers the same number of students -- 2 students per grade -- the probability of picking each grade is the same.
Thus, the problem can be rephrased as follows:
What is the probability that the two grades selected are freshman and sophomore?

P(first grade selected is freshman or sophomore) = 2/4. (Of the 4 grades, 2 are either freshman or sophomore.)
P(second grade selected is freshman or sophomore) = 1/3. (Of the 3 grades not yet selected, 1 will be freshman or sophomore.)
To combine these probabilities, we multiply:
2/4 * 1/3 = 1/6.

The correct answer is D.

[Jeff@TargetTestPrep]

In a high school debating team consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability that the students selected will consist one freshman and one sophomore?

A. 1/16
B. 1/8
C. 1/7
D. 1/6
E. 1/4

Let's start by finding the probability of choosing F - S, in this order. Since the probability of choosing one of the two freshmen from 8 available students is 2/8 = 1/4 and since the probability of choosing one of the two sophomores from the remaining 6 available students is 2/6 = 1/3, we have

P(F - S) = 1/4 x 1/3 = 1/12

A similar calculation can be made to find that the probability of choosing S - F, in this order, is also 1/12.

Thus, the probability that the team consists of one freshman and one sophomore is 1/12 + 1/12 = 1/6.

Answer: D