nsamp: Number of Samples from an Urn
In prob: Elementary Probability on Finite Sample Spaces

Description Usage Arguments Details Value Author(s) See Also Examples

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

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

`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.

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!].

A number.

G. Jay Kerns gkerns@ysu.edu.

urnsamples

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)

Loading required package: combinat

Attaching package: ‘combinat’

The following object is masked from ‘package:utils’:

    combn

Loading required package: fAsianOptions
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics
Loading required package: fOptions

Attaching package: ‘prob’

The following objects are masked from ‘package:base’:

    intersect, setdiff, union

[1] 9
[1] 6
[1] 3
[1] 6