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You work at the U.S. Mint, and you have access to an unlimited supply of four types of coins - pennies, nickels, dimes, and quarters. You are bored and would like to stack 11 (eleven) coins in a tower. The order of coins in the tower matters. You may assume that coins of the same type which are indistinguishable - any penny is the same as any other penny, and so on for all types. You can put any coin anywhere in the tower.
Please respond to the following questions. Note that you are always making a tower of 11 coins.
(a) How many possible towers are there?
(b) How many possible towers contain exactly four nickels?
(c) How many possible towers contain at least nine dimes?
(d) How many possible towers contain exactly two nickels AND exactly three quarters?
(e) How many possible towers contain exactly two nickels OR exactly three quarters? (Note that this includes the scenario of both at once. Be careful of overlapping cases!)
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