[1] A company with four principal corporate locations liked to rotate its senior staff among the [2] geographic locations: Atlanta (A), Baltimore (B), Chicago [C] and Dallas (D). Let N(A) represent the number of senior staff members spending time in Atlanta. Consider a sample space of only the top 100 senior staff. No one has spent time in both Baltimore and Chicago. And 40 have been exclusively Dallas. Chicago has seen a total of 20, with % of those seeing time in both Atlanta and Chicago, 10 spending time in Chicago and Dallas, and 5 spending time in Atlanta, Chicago and Dallas.Atlanta has had a total of 20 staff and 10 ofthose have spent time in Dallas. Exactly 36 total spent time in Baltimore with 3 of those spending time in Atlanta and Dallas as well , and 20 spending time in Baltimore alone .If 65 is the total spending time in Dallas ,what number spent time in both Dallas and Baltimore ;that is, N(D&B]? Nine indistinguishable treats are to be distributed among my three cats: Mochi, Binx, and Copper. (a) If each cat must get at least 1, how many ways can the nine treats be distributed? (b) With each cat still getting at least 1, what is the probability that Mochi ends up with 4? treats? [3] Will Byers, a character in Stranger Things often finds himself in an alternative world, the Upside Down. Will frequently oscillates in and out of this 4'\" dimension and is forever trying to avoid the Shadow Monster or one of its demogorgans in that alternative world. Will can move in an x or y manner and can also switch dimensions. We willtreat switching a dimension as if it were a step. Let's say that to hide behind a tree from the Shadow Monster in the Upside Down, that he must move from position (x, y, u) = {0,0,0} to (10,10,1l; that is, starting in our world, he moves to a position 10 steps away in x and y and also moves to the Upside Down (1). Being extremely scared, Will won't take anyr extra steps. He'll be perfectly efficient, taking only 21 positive moves toward his hiding place in the upside down. (a) How many paths (x, y, u} can Will take to his hiding place? (b) What is the probability that on the way to his hiding place, Will's passes through the location (4,4,1)? [4] A shiftyr gambler has three coins .One has tails on both sides ,one has heads on both sides , and one has tails on one side and heads on the other. The gambler grabs a coin at random from his pocket and flips it, with it coming to rest with heads up. What is the probability that the other side is tails