Counting 1: string enumeration

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Daniel Mansfield

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6 years, 2 months ago

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Daniel Mansfield 6 years, 2 months ago

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Daniel Mansfield 6 years, 2 months ago

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Daniel Mansfield 7 years, 7 months ago

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Name	Status	Author	Last Modified
Counting 1: string enumeration	Ready to use	Daniel Mansfield	13/02/2020 02:17
string enumeration	draft	Xiaodan Leng	10/07/2019 21:21
string enumeration	draft	Xiaodan Leng	10/07/2019 21:22
Counting: string enumeration	Ready to use	Stephen Maher	12/11/2020 08:29

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Question statement

A randomised string of $\var{n}$ digits is made using only the non-zero digits $1,2,3,4,5,6,7,8,9$ .

When each digit is chosen independently, the number of ways to choose the string is just the product of the number of ways to choose each of the digits.

# of ways to choose string = $\displaystyle \prod\limits_{i=1}^{\var{n}}$ (# ways to choose $i$ th digit).

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			Name	Type	Generated Value

ex1	number	886118
ex2	number	355967
n	integer	6
b	integer	7
c	integer	5

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Value

xxxxxxxxxx
 
sum(map(random(1..9)*10^k,k,0..(n-1)))

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Generated value: `number`

886118

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(a) # of ways to choose string $=$ $\displaystyle \prod\limits_{i=1}^{\var{n}}$ (# ways to choose $i$ th digit) $=$ $\displaystyle \prod\limits_{i=1}^{\var{n}} 9 = {9^\var{n} }$ .

(b) # of ways to choose string $=$ (# of ways of choosing an even digit) $\times$ (# of ways of choosing an odd digit) $\times \displaystyle \prod\limits_{i=3}^{\var{n}}$ (# ways to choose a digit less than $\var{b}$ ) $=$ $4 \times 5 \times {\var{b-1}^\var{n-2}}$ .

(c) # of ways to choose string $=$ (# of ways of placing the 9s) $\times$ (# of ways of placing the remaining digits) $=$ ${C(\var{n},\var{c})}\times 8^\var{n-c}$ .

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This question is used in the following exam:

Week 7: Counting by Daniel Mansfield in Discrete Mathematics.

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Daniel Mansfield 6 years, 2 months ago

Daniel Mansfield 6 years, 2 months ago

Daniel Mansfield 7 years, 7 months ago

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Generated value: `number`

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Counting 1: string enumeration

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Daniel Mansfield 6 years, 2 months ago

Daniel Mansfield 6 years, 2 months ago

Daniel Mansfield 7 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `number`