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Unformatted text preview: AMS 301.2 (Spring 2011) Homework Set # 8 Solution Notes # 10, 5.3: (a). We first give each person a pear, and now distribute 5 identical apples and 3 identical pears to 3 distinct people: parenleftbigg 5 + 3 1 5 parenrightbiggparenleftbigg 3 + 3 1 3 parenrightbigg (b). The apples can be distributed 3 5 ways, as each apple has 3 choices. The pears can be split either 1,1,4 (3 ways to choose who gets 4 pears) or 1,2,3 (3! ways to pick who gets 1 or 2 or 3 pears) and 2,2,2. Once we have the split, we can use Theorem 1. The final answer is: 3 5 (3 P (6; 1 , 1 , 4) + 3! P (6; 1 , 2 , 3) + P (6; 2 , 2 , 2)) # 12, 5.3: Here we break into cases depending on k { , 1 , 2 , 3 } , the number of balls we select out of the pink, lavender, and tan balls. This can be done in ( 3 k ) ways. Then we must select the remaining 8 k balls out of 3 types (red, white or blue), which can be done in ( 8 k +3 1 8 k ) ways (there are 8 k xs and 3 1 = 2 slashes). k can be any number between 0 and 3, so we sum...
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This note was uploaded on 05/28/2011 for the course AMS 301 taught by Professor Estie during the Spring '11 term at University of Florida.
 Spring '11
 Estie

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