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4.2. (a) How many n-tuples (x1,x2,...,xn) are there if the coordinates are required to be integers satisfying 0≤xi

4.2. (a) How many n-tuples (x1,x2,...,xn) are there if the coordinates are required to be integers satisfying 0≤xi

Advanced Engineering Mathematics
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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Letter (a) is the question.

4.2. (a) How many n-tuples (x₁, x2, . . . , xn) are there if the coordinates are required to be integers satisfying 0 ≤ xi < q? (b) Same question as (a), except now there are separate bounds 0 ≤ xi <qi for each coordinate. (c) How many n-by-n matrices are there if the entries xi,j of the matrix are integers satisfying 0≤xi, j < q? (d) Same question as (a), except now the order of the coordinates does not matter. So for example, (0, 0, 1, 3) and (1,0,3,0) are considered the same. (This one is rather tricky.) (e) Twelve students are each taking four classes, for each class they need two loose- leaf notebooks, for each notebook they need 100 sheets of paper, and each sheet of paper has 32 lines on it. Altogether, how many students, classes, notebooks, sheets, and lines are there? (Bonus. Make this or a similar problem of your own devising into a rhyme like the St. Ives riddle.)
Transcribed Image Text:4.2. (a) How many n-tuples (x₁, x2, . . . , xn) are there if the coordinates are required to be integers satisfying 0 ≤ xi < q? (b) Same question as (a), except now there are separate bounds 0 ≤ xi <qi for each coordinate. (c) How many n-by-n matrices are there if the entries xi,j of the matrix are integers satisfying 0≤xi, j < q? (d) Same question as (a), except now the order of the coordinates does not matter. So for example, (0, 0, 1, 3) and (1,0,3,0) are considered the same. (This one is rather tricky.) (e) Twelve students are each taking four classes, for each class they need two loose- leaf notebooks, for each notebook they need 100 sheets of paper, and each sheet of paper has 32 lines on it. Altogether, how many students, classes, notebooks, sheets, and lines are there? (Bonus. Make this or a similar problem of your own devising into a rhyme like the St. Ives riddle.)
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