CMSC 203 - Homework Assignment 3 - Due April 24, 2008
CMSC 203 - Homework Assignment 3 - Due April 24, 2008 CMSC 203 - Homework Assignment 3 - Due April 24, 2008
Name ___Solution Key_____CMSC 203 - Homework Assignment 3 - Due April 24, 20086. The Mars Candy Company sells bags of M&Ms with 64 pieces candy colored from 8 different colors.(a) How many different bags can they produce?Slots = 64, Types = 8, Restrictions = 0Total bags = C(Slots + Types - 1 - Restrictions,Slots - Restrictions) = C(64 + 8 - 1 - 0,64 - 0)= C(71,64) = 71! / (64! 7!)(b) How many different bags can they produce if each bag must contain at least 5 of each color?Slots = 64, Types = 8, Restrictions = 8(5) = 40Total bags = C(Slots + Types - 1 - Restrictions,Slots - Restrictions) = C(64 + 8 - 1 - 40,64 - 40)= C(31,24) = 31! / (24! 7!)
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Name ___Solution Key_____<strong>CMSC</strong> <strong>203</strong> - <strong>Homework</strong> <strong>Assignment</strong> 3 - <strong>Due</strong> <strong>April</strong> <strong>24</strong>, <strong>2008</strong>6. The Mars Candy Company sells bags of M&Ms with 64 pieces candy colored from 8 different colors.(a) How many different bags can they produce?Slots = 64, Types = 8, Restrictions = 0Total bags = C(Slots + Types - 1 - Restrictions,Slots - Restrictions) = C(64 + 8 - 1 - 0,64 - 0)= C(71,64) = 71! / (64! 7!)(b) How many different bags can they produce if each bag must contain at least 5 of each color?Slots = 64, Types = 8, Restrictions = 8(5) = 40Total bags = C(Slots + Types - 1 - Restrictions,Slots - Restrictions) = C(64 + 8 - 1 - 40,64 - 40)= C(31,<strong>24</strong>) = 31! / (<strong>24</strong>! 7!)
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