Counting 1: permutation and combination

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Name	Status	Author	Last Modified
Counting 1: permutation and combination	Ready to use	Daniel Mansfield	13/02/2020 02:15
permutation and combination	draft	Xiaodan Leng	10/07/2019 21:23
Counting: permutation and combination	Ready to use	Stephen Maher	12/11/2020 08:28

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Question statement

How many ways can you choose $r$ distinct objects from $n$ possible objects?

The answer depends upon whether the order of selection is important.

If the order of selection is important, then the number of ways to choose $r$ objects from $n$ is called a permutation $P(n,r) = \dfrac{n!}{(n-r)!}$ .
If the order of selection is not important, then the number of ways to choose $r$ objects from $n$ is called a combination $C(n,r) = \dfrac{n!}{(n-r)!r!}$ .

The NUMBAS syntax for $P(n,r)$ and $C(n,r)$ is perm(n,r) and comb(n,r).

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			Name	Type	Generated Value

a1	integer	4
a2	integer	7
a3	integer	9
n	integer	9
r	integer	5
r2	integer	5

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For part a, choosing $\var{r}$ from $\var{n}$ distinct objects when order matters can be done in $P(\var{n},\var{r}) = \var{perm(n,r)}$ ways.

For part b, choosing $\var{r2}$ from $\var{n}$ distinct objects when order does not matter can be done in $C(\var{n},\var{r2}) = \var{comb(n,r2)}$ ways.

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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, 1 month ago

Daniel Mansfield 6 years, 1 month ago

Daniel Mansfield 7 years, 6 months ago

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Counting 1: permutation and combination

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Daniel Mansfield 6 years, 1 month ago

Daniel Mansfield 6 years, 1 month ago

Daniel Mansfield 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`