) Compute the number of different sequences consisting of 3 x's, 4 y's, and 7 z's b) Compute the number of different walks from (1,1,1) to (3,5,7) if only unit steps in the positive x, positive y, or positive z directions are allowed.

) Compute the number of different sequences consisting of 3 x's, 4 y's, and 7 z's b) Compute the number of different walks from (1,1,1) to (3,5,7) if only unit steps in the positive x, positive y, or positive z directions are allowed.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

a) Compute the number of different sequences consisting of 3 x's, 4 y's, and 7 z's

b) Compute the number of different walks from (1,1,1) to (3,5,7) if only unit steps in the positive x, positive y, or positive z directions are allowed.

Please answer both parts as they are to one question.

The textbook answers are

a) 14!/(3!4!7!) b) 12!/(2!4!6!)

I think I can figure out part A but I would like someone to work it out just to double check. I would prefer part b if you will only answer one part. Thanks!

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