場合の数

number of cases

事象: event

根元事象: elementary event

余事象: complementary event

排反事象: exclusive event

$ _n\mathrm{P}_k = \frac{n!}{(n - k)!}

$ _n\mathrm{C}_k = \frac{_n\mathrm{P}_k}{k!} = \frac{n!}{k!(n - k)!}

$ \binom{n}{k} \coloneqq {}_n\mathrm{C}_k

$ ((n, k) -> prod((n-k+1):n))

code:jl

function permutation(n::Int, k::Int)

x = n = n - k + 1

n += 1

for _ in 1:k

x = x * n

n += 1

end

return x

end