COT 3100 Fall 2002 Homework #3 Assigned: 9/24/02 Due: 10/3/02 in lecture 1) Each of the following questions deals with permutations of TENNESSEE. a) How many permutations are there of the word TENNESSEE? b) How many of the permutations of TENNESSEE do not contain any occurences of contiguous vowels? c) How many permutations of TENNESSEE contain the substring EEEE? d) How many permutations of TENNESSEE contain all of the consonants in a single block? 2) The local ice cream shop serves 31 different flavors of ice cream. A sundae includes one scoop of any flavor ice cream, along with a syrup and a topping, both of which are optional. There are 5 different types of syrups and 12 different types of toppings. a) How many distinct sundaes can be ordered? (Note: a chocolate ice cream sundae without any syrup or topping should be counted separately from a chocolate ice cream sundae with chocolate syrup and no topping.) b) If a sundae is allowed to have three scoops of ice cream where each scoop must be
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