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 9.6 - Page 590: 4

Answer

4. n = 30, r = 8 (■(A@B)) = (A choose B) a. (■(30+8-1@30)) = (■(37@30))=37!/(30!*7!) = (31*32*33*34*35*36*37)/(2*3*4*5*6*7) = 10295472 b. (■(26+8-1@26)) = (■(33@26)) = 33!/(26!*7!) = (27*28*29*30*31*32*33)/(2*3*4*5*6*7) = 4272048 c. [ways with inventory of 30 batteries and at most 3 A7b batteries] = [ways with inventory of 30 batteries] – [ways with inventory of 30 batteries and at least 4 A7b batteries] = (■(37@30))- (■(33@26)) = 10295472- 4272048 = 6023424

Work Step by Step

4. n = 30, r = 8 (■(A@B)) = (A choose B) a. (■(30+8-1@30)) = (■(37@30))=37!/(30!*7!) = (31*32*33*34*35*36*37)/(2*3*4*5*6*7) = 10295472 b. (■(26+8-1@26)) = (■(33@26)) = 33!/(26!*7!) = (27*28*29*30*31*32*33)/(2*3*4*5*6*7) = 4272048 c. [ways with inventory of 30 batteries and at most 3 A7b batteries] = [ways with inventory of 30 batteries] – [ways with inventory of 30 batteries and at least 4 A7b batteries] = (■(37@30))- (■(33@26)) = 10295472- 4272048 = 6023424
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