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Number of combinations/permutations

combinatoricsCount.Rd

Calculate the number of combinations/permutations of a vector chosen \(m\) at a time with or without replacement. Additionally, these functions can calculate the number of combinations/permutations of multisets.

Usage

comboCount(v, m = NULL, ...)
permuteCount(v, m = NULL, ...)

# Default S3 method
comboCount(v, m = NULL, repetition = FALSE, freqs = NULL, ...)
# Default S3 method
permuteCount(v, m = NULL, repetition = FALSE, freqs = NULL, ...)

# S3 method for class 'table'
comboCount(v, m = NULL, ...)
# S3 method for class 'table'
permuteCount(v, m = NULL, ...)

Arguments

v

Source vector. If v is a positive integer, it will be converted to the sequence 1:v. If v is a negative integer, it will be converted to the sequence v:-1. All atomic types are supported (See is.atomic).

m

Number of elements to choose. If repetition = TRUE or freqs is utilized, m can exceed the length of v. If m = NULL, the length will default to length(v) or sum(freqs).

...

Further arguments passed to methods.

repetition

Logical value indicating whether combinations/permutations should be with or without repetition. The default is FALSE.

freqs

A vector of frequencies used for producing all combinations/permutations of a multiset of v. Each element of freqs represents how many times each element of the source vector, v, is repeated. It is analogous to the times argument in rep. The default value is NULL.

Value

A numerical value representing the total number of combinations/permutations.

Note

When the number of results exceeds \(2^{53} - 1\), a number of class bigz is returned.

See also

comboGeneral, permuteGeneral

Examples

## Same interface as the respective "general" functions:
## i.e. comboGeneral & permuteGeneral

permuteCount(-5)
#> [1] 120
permuteCount(5)
#> [1] 120
comboCount(25, 12)
#> [1] 5200300
permuteCount(15, 7, TRUE)
#> [1] 170859375
comboCount(25, 12, freqs = rep(2, 25))
#> [1] 458917850

## Return object of class 'bigz'
comboCount(250, 15, freqs = rep(2, 250))
#> Big Integer ('bigz') :
#> [1] 1035444613157684247678300