Answered: How many sequences of 6 positive digits…

Name: How many sequences of 6 positive digits (1-9) contain at most one even
Uploaded: 2024-03-20T06:38:58.000Z
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Description: How many sequences of 6 positive digits (1-9) contain at most one even digits?

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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How many sequences of 6 positive digits (1-9) contain at most one even digits?

Expert Solution

Step 1

Given number of digits in each sequence=6.

Number of digits which can be used= $(1 - 9)$

Number of even digits=2,4,6,8 ( 4 in number)

Number of odd digits=1,3,5,7,9 (5 in number)

Case 1) If repetition is not allowed ,

(i) If the sequence contains no even digits:

Number of ways of filling 5 odd digits in the 6 places of the sequence= $5 \times 4 \times 3 \times 2 \times 1 \times 0$

(ii) If the sequence contains 1 even digit:

Number of ways of filling 5 odd digits in the 6 places of the sequence $= 4! \times 5 \times 4 \times 3 \times 2 \times 1$

$= 2880$

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