Answer Happy

4. A Texas Hold'em poker tournament has 1557 players, in 9 distinct positions at 173 tables. Each table has a standard 52 card deck, and each player is dealt 2 cards. Hands are considered "the same” if they have the same rank of cards and same number of different suits. For example, the nine of hearts and three of hearts is the same as the nine of clubs and three of clubs, but neither are the same as the nine of spades and three of diamonds. (a) Show that there are two people in the tournament with the same starting hand and position. (b) Show that, for every position, there are two people with the same starting hand. (c) Show that there are two people who are dealt identical cards (not just "the same”, but with ranks and suits matching).