Counting
Part A:
Shinobi was so delighted the mission was a success that he hosted a small gathering with his friends. When his eight friends arrived at his house, they decided they would spend the night playing draw poker. Shinobi’s square dinner table was piled too high with snacks so they decided to play poker on his round table. Upon the arrival of the two last guests, Shinobi received many questions about his independent mission and the bounty he recovered. He instinctively became defensive towards the two guests, but had no evidence against them and couldn’t throw them out of his house. Instead, he decided that he would sit next to each of the two guests as the played poker to watch over them like a hawk.
If Shinobi insisted on sitting beside the two suspicious guests to keep an eye on them, how many ways can Shinobi and his eight guests be seated around the table?
Part B:
Finally after agonizing over the seating arrangements, Shinobi and his guests decided to start on their game of draw poker using a standard 52 card deck. After being dealt his first hand of five cards, Shinobi found himself in the following situations:
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