Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 9 - Counting and Probability - Exercise Set 9.5 - Page 583: 20

Answer

20. MILLIMICRON contains 2 M’s, 3 I’s, 2 L’s, 1 C, 1 R, 1 O, 1 N (■(A @ B)) = A choose B a. (■(11@2))(■(9@3))(■(6@2))(■(4@1))(■(3@1))(■(2@1))(■(1@1)) = 11!/2!9! * 9!/3!6! * 6!/2!4! * 4!/1!3! * 3!/1!2! * 2!/1!1! * 1!/1!0! = 5*11 * 7*4*3 * 5*3 * 4 * 3 * 2 * 1 = 11!/(2!3!2!1!1!1!1!) = 1663200 b. (■(9@1))(■(8@3))(■(5@2))(■(3@1))(■(2@1))(■(1@1)) = 9!/1!8! * 8!/3!5! * 5!/2!3! * 3!/1!2! * 2!/1!1! * 1!/1!0! = 9 * 7*8 * 2*5 * 3 * 2 * 1 = 9!/(1!3!2!1!1!1!) = 30240 c. (■(9@2))(■(7@3))(■(4@2))(■(2@1))(■(1@1)) = 9!/2!7! * 7!/3!4! * 4!/2!2! * 2!/1!1! * 1 = 36 * 35 * 6 * 2 = 9!/2!3!2!1!1! = 2*5*3*7*8*9 = 15120

Work Step by Step

20. MILLIMICRON contains 2 M’s, 3 I’s, 2 L’s, 1 C, 1 R, 1 O, 1 N (■(A @ B)) = A choose B a. (■(11@2))(■(9@3))(■(6@2))(■(4@1))(■(3@1))(■(2@1))(■(1@1)) = 11!/2!9! * 9!/3!6! * 6!/2!4! * 4!/1!3! * 3!/1!2! * 2!/1!1! * 1!/1!0! = 5*11 * 7*4*3 * 5*3 * 4 * 3 * 2 * 1 = 11!/(2!3!2!1!1!1!1!) = 1663200 b. (■(9@1))(■(8@3))(■(5@2))(■(3@1))(■(2@1))(■(1@1)) = 9!/1!8! * 8!/3!5! * 5!/2!3! * 3!/1!2! * 2!/1!1! * 1!/1!0! = 9 * 7*8 * 2*5 * 3 * 2 * 1 = 9!/(1!3!2!1!1!1!) = 30240 c. (■(9@2))(■(7@3))(■(4@2))(■(2@1))(■(1@1)) = 9!/2!7! * 7!/3!4! * 4!/2!2! * 2!/1!1! * 1 = 36 * 35 * 6 * 2 = 9!/2!3!2!1!1! = 2*5*3*7*8*9 = 15120
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