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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct? In other words, how many 5-tuples of integers (h, i, j, k, m) are there with 1shsisjsksms n?

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct? In other words, how many 5-tuples of integers (h, i, j, k, m) are there with 1shsisjsksms n?

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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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct? In other words, how many 5-tuples of integers (h, i, j, k, m) are there with 1shsisjs ksms n? As in Example 9.6.3, you can represent any ordered 5-tuple of integers (h, i, j, k, m) with 1 s hsisjsksm sn as a string of n- 1 vertical bars and 5 v crosses, with the position of crosses indicating which 5 v integers from 1 to n are (n(n+1) (n+2)(n+ 3)(n+ 4)) included in the 5-tuple. Thus, the number of 5-tuples is the same as the number of strings of vertical bars and crosses, which is 120
Transcribed Image Text:If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct? In other words, how many 5-tuples of integers (h, i, j, k, m) are there with 1shsisjs ksms n? As in Example 9.6.3, you can represent any ordered 5-tuple of integers (h, i, j, k, m) with 1 s hsisjsksm sn as a string of n- 1 vertical bars and 5 v crosses, with the position of crosses indicating which 5 v integers from 1 to n are (n(n+1) (n+2)(n+ 3)(n+ 4)) included in the 5-tuple. Thus, the number of 5-tuples is the same as the number of strings of vertical bars and crosses, which is 120
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