Justification Socks: Algorithmic Explanations for Socks 8-10

Justification Socks is a series that delves into the intricacies of sock algorithms 8-10. Here's what these enigmas have to offer:

Algorithm 8: The Sock Drawer Conundrum

When faced with a drawer containing 5 socks of different colors, how many combinations can one achieve by selecting 2 socks at random? The answer, my friend, is a whopping 10! But don't just take our word for it, click here for the proof!

Algorithm 9: The Pairing Paradox

What happens when you have 3 pairs of socks and 1 lone sock? Do you pair the lone sock with its matching pair, or do you leave it alone? The answer, much like the socks themselves, is a tangled web of complexity. Dive deeper into the paradox!

Algorithm 10: The Sock Drawer Optimization Problem

Given a sock drawer containing 15 pairs of socks and a 50% chance of a sock being a mirror image of its pair, what is the expected number of socks that will be in the "sock-p prophets" category? Uncover the secrets of the sock drawer!

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