The "Birthday Problem" Note: Before attempting this problem, make sure to read about permutations and combinations (or make your way through the Knewton problems) The big question we're trying to answer is this: "What's the probability that two people in a room of 25 people have the same birthday?". If you've been working with probability for a bit, you might guess that it's (1/365)*(1/365).That would be the probability that two people both are born on, say, January 1st. This problem is a bit more complicated because there's 25 people, and they can share any birthday together.

Here's some steps to walk you through the calculation! 1. How many ways can 25 people be paired up? In other words, give 25 people their own letter of the alphabet. How many ways can you pair up the letters? You could have AB, AC, BD, EH, etc. State how many ways this can be done and support your answers with mathematics. (Hint:The order does not matter. We don't want to double count a pair: Andrew-Sarah is the same as Sarah-Andrew).

2. Randomly pick any two people from the room of 25. What's the chance of those two having the same birthday? Again, including the number and a sentence or two for how you arrived at this number will suffice. Assume two separate birthdays are independent.

3. What are the chances that those two people do not have the same birthday? Include any steps in your calculation. (Hint: the complement rule. If the probability of rain is 0.30, the probability of no-rain is 0.70.)

4. What's the chance that no pairs have the same birthday? You're considering the number of pairs from step 1, each with a probability of occurrence that you found in step 3. Include any steps in your calculation: No sentences required (Hint: The probability of flipping a coin and getting "heads" is

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