Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.5 - Generalized Permutations and Combinations - Exercises - Page 433: 38

Answer

a) 4,705,360,871,073,570,227,520. b) 196,056,702,961,398,759,480

Work Step by Step

a) When boxes are distinguishable, then in the 1st box issues can be chosen in (40,10) For the Second box, only 30 issues remain so it can be chosen in C(30,10) Similarly, for 3rd and 4th box, we have C(20,10) and C(10,10) respectively. Using product rule we get C(40,10)$\times$C(30,10)$\times$C(20,10)$\times$C(10,10) = $\frac{40!}{10!^{4}}$ = 4,705,360,871,073,570,227,520. b) When boxes are identical we divide the previous solution by 4! so the solution becomes $\frac{40!}{10!^{4}.4!}$ =196,056,702,961,398,759,480
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