john and james are among 30 students who have applied for a trip to boy's state. two students from the group will be selected at random from the trip. what is the probability that john and james will be the 2 students selected?

number of possible pairs that can be chosen

= C(30,2) = 435
prob(John , James) = 1/435

To find the probability that John and James will be the two students selected for the trip, we need to know the total number of possible outcomes and the number of favorable outcomes.

There are 30 students in total who have applied for the trip. From this group, we need to select two students at random.

The total number of possible outcomes can be found using combinations. Since we need to select two students from a group of 30, the total number of possible outcomes is given by:

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

where n is the total number of students (30 in this case) and r is the number of students to be selected (2 in this case).

C(30,2) = 30! / (2!(30-2)!) = 30! / (2!28!)

Simplifying, we get:

C(30,2) = (30 * 29 * 28!) / (2 * 1 * 28!) = 435

So, there are 435 possible outcomes when two students are selected randomly from the group of 30.

Now, let's determine the number of favorable outcomes, i.e., the number of ways John and James can be selected.

Since John and James need to be selected, we have only one option for John and one option for James. Therefore, the number of favorable outcomes is 1.

The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 435

Therefore, the probability that John and James will be the two students selected is 1/435.