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 432: 23

Answer

7484400 ways

Work Step by Step

The number of ways 2 objects can be placed into 1st box= $C$(12,2) The number of ways 2 objects can be placed into 2nd box= $C$(10,2) ... Similarly, for the last box, we have only 2 objects, so the number of ways becomes $C$(2,2) All the boxes are distinguishable So total Number of ways = $C$(12,2)$\times$ $C$(10,2)$\times$ ....$C$(2,2) = $\frac{12!}{(2!)^{6}}$ =7484400 ways.
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