Birthday Paradox Math Project

I am currently taking precalc and have a math project due. After flipping from topic to topic I finally settled for the birthday paradox. I see that the solution for the birthday paradox itself may be too simple for a project, but I found this paper that also discusses the approximation of the birthday paradox. Probability isn't one of my strong points, and some of the explanations are confusing for me:

1) There is an intuitive reason why the probability of matching birthdays is so high. The probability that a given pair of students have the same birthday is only 1/365. This is very small. But with around two dozen students, we have around 365 pairs of students, and the probability one of these 365 attempts will result in an event with probability 1/365 gets to be about 50-50. With 100 students there are about 5000 pairs, and it is nearly certain that an event with probability 1/365 will occur at least once in 5000 tries.

***I don't understand this explanation...how is it that 24 students is equivalent to 365 pairs of students?** The statements afterwards confuse me as well :(

2) I am interested in adding the approximation part into my project but I have **no idea what an approximation really is for**... what is the difference between it and the solution? This is the link to the paper..birthday problem starts on page 42:

http://ocw.mit.edu/NR/rdonlyres/Elec...AC2/0/ln10.pdf

-Being in high school, **am I over my head with the approximation part?** If not, do you have recommendations of what I should research to help myself better understand it? for ex. I don't understand what 1-x = e2 is for.

**I know this is a lot of information and a mouthful to read but any help would be greatly appreciated :)**