Math 2230 Assignment 2 Solutions S16

Math 2230 Assignment 2 Solutions S16 - Math 2230 Assignment...

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Math 2230 Assignment # 2 Solutions 1. A bakery sells 3 types of donuts; Long John, Boston Cream, and Cholcolate Glaze. If the bakery has 3 Long Johns, 5 Boston Creams, and 7 Chocolate Glazed, how many ways are there to order 12 donuts? Solution: Let S be the set of all ways to order 12 donuts of these three types where the amount of each is unlimited. Let c 1 be the condition that the order contains more than 3 Long Johns. Let c 2 be the condition that the order contains more that 5 Boston Cream. Let c 3 be the condition that the order contains more than 7 chocolate glazed. N = | S | = 12 + 3 - 1 3 - 1 = 14 2 . N ( c 1 ) = 10 2 , N ( c 2 ) = 8 2 , N ( c 3 ) = 6 2 . N ( c 1 c 2 ) = 4 2 , N ( c 1 c 3 ) = 2 2 , N ( c 2 c 3 ) = 0. N ( c 1 c 2 c 3 ) = 0. N = 14 2 - 10 2 + 8 2 + 6 2 + 4 2 + 2 2 + 0 - 0 = 10. 2. Consider strings of 12 lowercase letters, such as agsajmnuuyio . How many strings either are a repetition of 2 strings of 6, such as asdfghasdfgh , or a repetition of three strings of 4, such as qwerqwerqwer , or read the same forwards as backwards, such as zxcvbnnbvcxz?
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