Permutations and Combinations

## Description

The following Sage interact computes

(1)\begin{align} _n P_r = \frac{n!}{(n - r)!} \quad \text{and} \quad _n C_r = \frac{n!}{r!(n - r)!}. \end{align}

The default values are $n = 5$ and $r = 2$.

## Sage Cell

#### Code

```
@interact
def _(n = input_box(default=5), r=input_box(default=2)):
P = factorial(n)/factorial(n - r)
C = P/factorial(r)
pretty_print(html(r"$n = %s$" %n))
pretty_print(html(r"$r = %s$" %latex(r)))
pretty_print(html(r"${}_n P_r = %s$" % latex(P)))
pretty_print(html(r"${}_n C_r = %s$" %latex(C)))
```

## Options

None

## Tags

Primary Tags: interacts, combinatorics

Secondary Tags: permutations, combinations

## Related Cells

None

## Attribute

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Author: T. Judson

Date: 21 Jul 2017 08:20

Submitted by: Tom Judson