How to compute nPr in sagemath

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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))

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!