# How to compute nPr in sagemath

How to compute nPr in sagemath? Please help

How to compute nPr in sagemath

How to compute nPr in sagemath? Please help

1

The following method avoids computing factorials explicitly, which can be computationally expensive for large values of n and r. Instead, it computes the product of a sequence of values using a generator expression, which is more memory-efficient and faster than computing factorials. You can compute perm(n, r) using a `prod`

function, which is a built-in SageMath function that computes the product of a sequence of values.

See the code:

```
perm(n, r) = prod(n - i for i in range(r))
```

0

Hello! I am assuming nPr means "n permutation r". Unfortunately, SageMath doesn't have a command for that purpose. However, if you remember that

$$nPr = \frac{n!}{(n-r)!} = \binom{n}{r}r!,$$

you can make something like this:

```
perm(n, r) = factorial(n) / factorial(n - r)
```

or even:

```
perm(n, r) = binomial(n, r) * factorial(r)
```

Hope this helps!

To my surprise, the former is about 12 times faster than the latter :

```
sage: %timeit Permutations(5,3).cardinality()
2.31 µs ± 450 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
sage: sage: %timeit binomial(5,3)*factorial(3)
27.3 µs ± 860 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
```

Go figure...

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Asked: ** 2023-07-15 13:42:28 +0200 **

Seen: **263 times**

Last updated: **Jul 21 '23**

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What is nPr?