A fish store is setting up an aquarium contest. Each entry has to feature one of 10 types of fish. Each entry has to feature one of 5 types of sand. Each entry is one of three sizes (small, regular or large) . Amazingly, they received exactly one entry for each possible combination of fish type, sand type, and size. [Answers may be left in unsimplified binomial notation.] (a) How many entries are there? (b) They need to pick a set of 6 entries to be finalists for the contest. i. How many ways can they pick 6 entries so that there are 3 fish types, two entries of each fish? ii. How many ways can they pick 6 entries so that there are 3 fish types, each with a different number of entries? (So 1,2, and 3 entries for the fish.) iii. How many ways can they pick 6 entries so that there is at least one of each sand type? (c) They decide to display 7 of the entries on (installed, ordered) pedestals in the store. i. How many different arrangements of 7 entries will have only small tanks? ii. How many different arrangements of 7 entries will have no repeated fish types