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: 23

Answer

$14 \choose 7 $$= 3432$

Work Step by Step

To get to the final point, the rook must make 7 moves right and 7 moves up in total. All that remains is to order the moves. The number of ways to do this is $14 \choose 7$, as we can think of this as choosing 7 spots in the overall sequence to put the "up" moves, and the right moves will just fill the remaining spaces. Therefore, the answer is $14 \choose 7 $$= 3432$.
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