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1. (20 points) (a) (10 points) Consider a 10card poker hand. A special type of hand that has three denominations repeated three times and the last denomination repeated once is called a chill house. For example King of Diamonds, King of Hearts, King of Spades, 5 of Clubs, 5 of Hearts, 5 of Spades, 2 of Clubs, 2 of Diamonds, 2 of Spades, Jack of Hearts is a chill house. What is the probability that in a randomly dealt hand, Where all (\"1%) hands are equally likely, we get a chill house? (You can leave your answer in a form with binomial coeicients.) (b) (10 points) Consider the following 9 x 9 grid of cities. Assume that a travelling salesman named Tod Packer is to go from city B (top right corner) to city A (bottom left corner), while taking only either "left" (L) steps or "down" (D) steps, a total of 18 steps. B C A Assuming Tod chooses such a path at random (each possible path equally likely), what is the probability that he will go through city C? (HINT: First, find the total number of paths. How many of each of the "L" and "D" steps does this person need to go from B to A? After that, restrict the paths to go through C. You can leave your answer in a form with binomial coefficients.)