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

## Description

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

## Usage

 `1` ```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!].

A number.

## Author(s)

G. Jay Kerns gkerns@ysu.edu.

`urnsamples`

## Examples

 ```1 2 3 4``` ```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) ```

### Example output

```Loading required package: combinat

Attaching package: ‘combinat’

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

combn

Attaching package: ‘prob’

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

intersect, setdiff, union

 9
 6
 3
 6
```

prob documentation built on May 2, 2019, 12:20 p.m.