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How many 5-tuples (x1, x2, x3, x4, X5) of positive integers from 1 to n are there? How many 5-tuples (x1, x2, x3, x4, X3) of positive integers from 1 to n without repeated elements? How many 5-tuples (x1, x2, x3, x4, X3) of positive integers from 1 to n are there such that xı < x2 < x3 < x4 < x5?

How many 5-tuples (x1, x2, x3, x4, X5) of positive integers from 1 to n are there? How many 5-tuples (x1, x2, x3, x4, X3) of positive integers from 1 to n without repeated elements? How many 5-tuples (x1, x2, x3, x4, X3) of positive integers from 1 to n are there such that xı < x2 < x3 < x4 < x5?

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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Discrete Mathematics: Counting.

Please check the image for the question.

. (a) How many 5-tuples (x1, x2, X3, X4, X5) of positive integers from 1 to n are there? (b) How many 5-tuples (x1, 2, x3, X4, X5) of positive integers from 1 to n without repeated elements? (c) How many 5-tuples (x1,x2, X3, X4, 05) of positive integers from 1 to n are there such that x1 < x2 < x3 < x4 < x5? (d) How many 5-tuples (x1, x2, x3, X4, X5) of positive integers from 1 to n are there such that x1 < x2 < x3 < x4 < x5? (e) A 5-tuple from those described in part (d) is chosen at random. What is the probability that it has no repeated element?
Transcribed Image Text:. (a) How many 5-tuples (x1, x2, X3, X4, X5) of positive integers from 1 to n are there? (b) How many 5-tuples (x1, 2, x3, X4, X5) of positive integers from 1 to n without repeated elements? (c) How many 5-tuples (x1,x2, X3, X4, 05) of positive integers from 1 to n are there such that x1 < x2 < x3 < x4 < x5? (d) How many 5-tuples (x1, x2, x3, X4, X5) of positive integers from 1 to n are there such that x1 < x2 < x3 < x4 < x5? (e) A 5-tuple from those described in part (d) is chosen at random. What is the probability that it has no repeated element?
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