Counting Problem 1

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Johnathan Gregg

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Johnathan Gregg

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Needs to be tested

4 years, 11 months ago

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Johnathan Gregg 4 years, 11 months ago

Gave some feedback: Needs to be tested

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Johnathan Gregg 4 years, 11 months ago

Published this.

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Johnathan Gregg 4 years, 11 months ago

Created this.

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Question statement

Note: In this question please give full answers, do not round your results.

A group of {boys} boys and {girls} girls sit on a bench. Determine the number of possible arrangements, given that

Give any introductory information the student needs.

			Name	Type	Generated Value

words	list	List of 11 items
b	integer	9
g	integer	2
boys	string	nine
girls	string	two
ans_a	number	32659200
ans_b	number	26127360
ans_c	number	20321280

Automatically regenerate variables?

Name

Data type

Value

(text strings)

Description

to convert number to words

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ "zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten" ]

This variable doesn't seem to be used anywhere.

Advice

In part (a) you can work out the total number of arrangements $\var{(b+g)}!$ and subtract the arrangements which involve the girls sitting together $2! \times \var{b+1}!$

$\var{(b+g)}! - 2 \times \var{b+1}! = \var{ans_a}$

In part (b) you can imagine placing two boys at either end and then you have $\var{b}$ places left to fill with anyone.

$\var{b} \times \var{b-1} \times \var{b}!= \var{ans_b}$

In part (c) you can combine the logic from the previous two steps

$\var{b} \times \var{b-1} \times (\var{b}! -2 \times \var{b - 1}! )= \var{ans_c}$

Give a worked solution to the whole question.

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Part	Test	Passed?
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

End of Year IB1 Exam HL by Johnathan Gregg in Johnathan's workspace.
End of Year Exam by Johnathan Gregg in Johnathan's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Number entry

Advanced settings

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Counting Problem 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Number entry

Advanced settings

Generated value: `list`