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Laney invites 2 friends over for her birthday including Prof. Bagley. Keith bakes a vegan chocolate cake, which is delicious, and cuts it into 8 identical pieces. Show all your work. Give each answer as a whole number (XX) or as a percent (XX.YY%).

A) How many ways are there to distribute the 8 pieces among the three people at the party?

B) How many ways are there to distribute the 8 pieces among the group such that Laney, personally, gets at least 4 pieces?

C)Assume that each person can eat a maximum of 5 pieces. Given this limitation, how many ways are there to distribute the 8 pieces among the three people?

D) Suppose all 8 pieces will be distributed. What is the probability that Laney and Keith get the same number of pieces?

E) Suppose Dean Beth joins the party, and brings another cake; this one is vanilla, and also cut into 8 identical pieces. How many ways are there to distribute all 16 pieces from both cakes to Laney and Keith (no one else gets any cake in this scenario)?