nsamp: Number of Samples from an Urn

In probs: Elementary Probability on Finite Sample Spaces

Number of Samples from an Urn

Description

Calculates the number of samples from an urn under different sampling scenarios.

Usage

nsamp(n, k, replace = FALSE, ordered = FALSE)

Arguments

n	an integer or integer vector.
k	an integer or integer vector.
replace	logical indicating whether sampling should be done with replacement.
ordered	logical indicating whether order among samples is important.

Details

The nsamp() function will calculate the number of samples from an urn under assorted assumptions on the sampling procedure. The arguments are: n, the number of (distinguishable) objects in the urn, k, the sample size, and replace, ordered as documented in urnsamples.

nsamp() is vectorized, so that entering vectors instead of numbers for n, k, replace, and ordered results in a vector of corresponding answers.

The formulas used in the four possible combinations of replace and ordered are as follows:

• When replace = TRUE and ordered = TRUE, the value is n^k.

• When replace = FALSE and ordered = TRUE, the value is n!/(n-k)!.

• When replace = FALSE and ordered = FALSE, the value is n!/[k!(n-k)!].

• When replace = TRUE and ordered = FALSE, the value is (n-1+k)!/[(n-1)!k!].

Value

A number.

Author(s)

G. Jay Kerns [e-mail].

See Also

urnsamples

Examples

nsamp(n = 3, k = 2, replace = TRUE, ordered = TRUE)
nsamp(n = 3, k = 2, replace = TRUE, ordered = FALSE)
nsamp(n = 3, k = 2, replace = FALSE, ordered = FALSE)
nsamp(n = 3, k = 2, replace = FALSE, ordered = TRUE)

probs documentation built on June 22, 2024, 10:41 a.m.