01. Number of ways of choosing subsets with a condition

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Martina Balagovic

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1 year, 6 months ago

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Martina Balagovic 1 year, 6 months ago

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Martina Balagovic 1 year, 6 months ago

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Martina Balagovic 1 year, 6 months ago

Created this as a copy of Number of ways of choosing subsets with a condition.

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Question statement

A company has $\var{t}$ employees, $\var{m}$ of them male and $\var{f}$ female. We need to form a committee of $\var{n}$ employees.

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			Name	Type	Generated Value

n	integer	7
m	integer	11
t	integer	20
f	integer	9
ans1	number	77154
ans2	number	73032
ans3	number	542640
ansA	number	77520

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xxxxxxxxxx
 
random(5..7)

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Generated value: `integer`

→ Used by:

ans1
ans2
ans3
ansA

This variable doesn't seem to be used anywhere.

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Part b) Gap-fill
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Part c) Gap-fill
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How many ways are there to form such a committee? Number of ways to form a committee is Unnamed gap.

Advice

a)

There are $\displaystyle \binom{\var{t}}{\var{n}}=\var{ansA}$ in which to form the committee when there are no conditions on the number of male and female employees needed.

b)

There are $\displaystyle \binom{\var{t}}{\var{n}}$ ways to form the committee when there are no conditions on the number of male and female employees needed. There are $\displaystyle \binom{\var{f}}{\var{n}}$ ways to form a committee with no male employees in it, and there are $\displaystyle \binom{\var{m}}{\var{n}}$ ways to form a committee with no female employees in it. This gives a total of $\displaystyle \binom{\var{t}}{\var{n}}-\displaystyle \binom{\var{f}}{\var{n}}-\displaystyle \binom{\var{m}}{\var{n}}=\var{ans1}$ ways to form a committee with at least one male and one female employee in it.

There are $\displaystyle \binom{\var{t}}{\var{n}}$ ways to form the committee when there are no conditions on the number of male and female employees needed. There are $\displaystyle \binom{\var{m}}{\var{n}}$ ways to form a committee with no female employees in it. There are $\displaystyle \binom{\var{m}}{\var{n-1}}\cdot {f}$ ways to form a committee with exactly one female employee in it. This gives a total of $\displaystyle \binom{\var{t}}{\var{n}}-\displaystyle \binom{\var{m}}{\var{n}}-\displaystyle \binom{\var{m}}{\var{n-1}}\cdot \var{f}=\var{ans2}$ ways to form a committee with at least two one female employees in it.

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This question is used in the following exams:

Assessment For Maths Tutor by John Gaius in John's workspace.
MAS1701 exam Sem 1 2023/24 by Martina Balagovic in NCL MAS1701.
Past paper 23-24 by Martina Balagovic in NCL MAS1701.

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01. Number of ways of choosing subsets with a condition

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Martina Balagovic 1 year, 6 months ago

Martina Balagovic 1 year, 6 months ago

Martina Balagovic 1 year, 6 months ago

Martina Balagovic 1 year, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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b)

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01. Number of ways of choosing subsets with a condition

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Martina Balagovic 1 year, 6 months ago

Martina Balagovic 1 year, 6 months ago

Martina Balagovic 1 year, 6 months ago

Martina Balagovic 1 year, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`