Neighborhood Celebrations For each of these problems, write down the permutation/combination expression and then sim-

plify to a final number.

In New York, the people from Inwood Hill and Washington Heights come together for a neighbrhood dinner. Every year, 20 people come from Inwood Hill and 15 people come from Washington Heights.

1. In 2011, there were two tables set up, one for Inwood Hill people and another for Washington Height people. All people must sit at the table for their neighborhood. How many ways can the people sit at these dinner tables. Two table setups are the same if all of the people in both setups are in the same order.

2. In 2012, to further bolster community, there was one table set up so everyone can sit together. In addition, it was declared no two Washington Heights people could sit next to each other. How many ways can this table setup be made? Two table setups are the same if all of the people in both setups are in the same order.

3. In 2014, the neighborhoods decided to add fun street games like relay dominoes. Two teams of 5 people must be made from all the people at the dinner. How many ways can these teams be made?

4. In 2015, rules were added so the teams would always have a combination of Inwood Hill people and Washington Heights people. The teams were named "Yankees" and "Mets". The "Mets" must have at least 3 people from Inwood Hill. The "Yankees" must have more Inwood Hill people than the "Mets". Given these rules, how many ways can these two teams be made under these rules?