a) A business gets a keypad door lock. The lock has digits from zero to nine and a set code can be the length of 4. How many options exist for employee ID's if the first digit cannot be a 0 and the remaining digits must be different from one another? Show your work and explain.

b) Its Halloween and everyone is out trick-or-treating. There are 20 candies given to 60 kids. Assuming all the candies are the same and that each kid can only get 1 candy maximum, how many ways can the candies be distributed? Show your work and explain.

c) A pouch contains a set of rocks. Each rock is either black, grey, white, or brown. How many rocks must be in the bag to garuntee that there are at least 6 rocks of the same color? Show your work and explain.

d) A neighborhood street has 6 houses on it. Each house has 5 rooms and only 1 room is empty in each of them. If a person randomly walks into each house and only goes into 1 room per house, what is the probability that they walk into at least 2 empty rooms? Explain without combination or permutation notation.