Closed runebone closed 1 year ago
$$ Pr(k-perm\ in\ n) = \frac{n}{n} \cdot \frac{n-1}{n} \cdot \frac{n-2}{n} \dots \frac{n-k+1}{n} $$
$$ Pr(k-perm\ in\ n) = \frac{\frac{n!}{(n-k)!}}{n^k} = \frac{n!}{n^k (n-k)!} $$
Which is indeed the complementary event to the birthday problem. You can check https://en.wikipedia.org/wiki/Birthday_problem
Thanks!
$$ Pr(k-perm\ in\ n) = \frac{n}{n} \cdot \frac{n-1}{n} \cdot \frac{n-2}{n} \dots \frac{n-k+1}{n} $$
$$ Pr(k-perm\ in\ n) = \frac{\frac{n!}{(n-k)!}}{n^k} = \frac{n!}{n^k (n-k)!} $$
Which is indeed the complementary event to the birthday problem. You can check https://en.wikipedia.org/wiki/Birthday_problem