In this problem, we are dealing with two dimensional arrays (or matrices) that have 10 rows and 10 columns. Further, each entry in the array is 1, 2, or 3. Assume that the rows as well as columns are indexed by 1 through 10. Recall that there are 3100 such matrices. (a) In how many such matrices every row has exactly 5 ones and there are no other restrictions? (b) Imagine the matrix to be divided into 4 quadrants. In how many such matrices, in every quadrant there are exactly 10 ones and there are no other restrictions?

In this problem, we are dealing with two dimensional arrays (or matrices) that have 10 rows and 10 columns. Further, each entry in the array is 1, 2, or 3. Assume that the rows as well as columns are indexed by 1 through 10. Recall that there are 3100 such matrices. (a) In how many such matrices every row has exactly 5 ones and there are no other restrictions? (b) Imagine the matrix to be divided into 4 quadrants. In how many such matrices, in every quadrant there are exactly 10 ones and there are no other restrictions?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section: Chapter Questions

Problem 12RP

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