#include #define rep(i,a,b) for(int i=a;i=b;i--) #define fore(i,a) for(auto &i:a) #pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } //--------------------------------------------------------------------------------------------------- /*---------------------------------------------------------------------------------------------------             ∧_∧       ∧_∧  (´<_` )  Welcome to My Coding Space!      ( ´_ゝ`) /  ⌒i     /   \    | |     /   / ̄ ̄ ̄ ̄/  |   __(__ニつ/  _/ .| .|____      \/____/ (u ⊃ ---------------------------------------------------------------------------------------------------*/ int F, N, K; //--------------------------------------------------------------------------------------------------- void _main() { cin >> F >> N >> K; double ans = 0; rep(x, 1, F + 1) { double p1 = (double)(F - x) / (double)F; double p2 = 1.0 / (double)F; double p3 = 1 - (p1 + p2); double p = 0; rep(i, 0, K) rep(j, 0, N - i + 1) { if (i + j < K) continue; int k = N - (i + j); // より大きい数がi回、同じ数がj回、より小さい数がk回 double pp = 1; rep(a, 0, i) pp *= p1; rep(a, 0, j) pp *= p2; rep(a, 0, k) pp *= p3; rep(a, 0, N) pp *= (a + 1); rep(a, 0, i) pp /= (a + 1); rep(a, 0, j) pp /= (a + 1); rep(a, 0, k) pp /= (a + 1); p += pp; } ans += x * p; } printf("%.10f\n", ans); }