combinatorics {exams.forge}

Combinatorics

Description

• permutation computes the number of permutations

• variation computes the number of variations with and without replication

• combination computes the number of combinations with and without replication

• combinatorics computes all combinatorics results for k < n and returns it as list of:

  permutation.n

  P(n)

  permutation.k

  P(k)

  permutation.nk

  P(n; k)

  variation

  V(n;k)

  variation.rep

  V^W(n;k)

  combination

  K(n;k)

  combination.rep

  K^W(n;k)

• lfact computes the natural logarithm of the factorial of a given number n

• lfactquot calculates the natural logarithm of the quotient of factorials

• lbinom computes the natural logarithm of the binomial coefficient, "n choose k"

Usage

combinatorics(n, k)

variation(n, k, repl = FALSE)

combination(n, k, repl = FALSE)

permutation(n, k = rep(1, n))

lfact(n)

lfactquot(n, ...)

lbinom(n, k)

combo(n, k, repl = FALSE)

combs(n, k)

fact(n)

factquot(n, ...)

binom(n, k)

Arguments

n

numeric: total number of elements

k

numeric: number of elements to choose

repl

logical: with repetition (default: FALSE)

...

numeric: further arguments for lfactquot

Value

A list.

Examples

permutation(8)
permutation(8, c(1,3,2,2))
combination(8, 4)
combination(8, 4, TRUE)
variation(8, 4)
variation(8, 4, TRUE)
combinatorics(8, 4)