Let's break down this problem step-by-step:

1. We know there are 100 people in the room.
2. 90 of these people have blue eyes, so the remaining 10 people must have green eyes.
3. We want to find the probability of picking two people with green eyes.

To calculate this probability, we can use the formula for combinations:
Probability = (number of successful outcomes) / (total number of possible outcomes)

4. The total number of ways to choose two people out of 100 is given by the combination formula: C(100, 2) = 100! / (2! * 98!) = 4950
5. The number of successful outcomes (picking two people with green eyes) is given by the combination formula: C(10, 2) = 10! / (2! * 8!) = 45

Now, we can plug these values into our probability formula:
Probability = 45 / 4950

6. Simplify the fraction: Probability = 1 / 110

So, the probability of picking two people with green eyes is 1/110.
There are 100 people in a room. 90 of them have blue eyes, and the rest have green eyes. If we randomly pick two people from the room, what is the probability that both of them have green eyes?