Thank you please answer the first part as well as the second part

1. Hash Table Probabilities (3 points) (1) (1 point) Suppose 2 keys are inserted into an empty hash table with m slots. Assuming simple uniform hashing, what is the probability of: (a) exactly 0 collisions occurring (b) exactly 1 collisions occurring (2) (2 points) Suppose 3 keys are inserted into an empty hash table with m slots. Assuming simple uniform hashing, what is the probability of: a) exactly 0 collisions occurring (b) exactly 1 collisions occurring (c) exactly 2 collisions occurring 2. Red-Black Trees (2 points) (1) Company X has created a new variant on red-black trees which also uses blue as a color for the nodes. They call these "red-black-blue trees". Be- low are the new rules for these trees: . Every node is red, blue, or black The root is black . Every leaf (NIL) is black. If a node is red, then both its children are black If a node is blue, then both its children are red or black. . For each node, all simple paths from the node to descendant leaves con- tain the same number of black nodes (a) (2 points) In class we found that the height, h, of a red-black tree is