/** * author: ivanzuki * created: Fri Sep 24 2021 **/ #include using namespace std; const int S = 55; const int M = 155; double dp[S][S][S][S]; int main() { ios_base::sync_with_stdio(false); cin.tie(0); vector> Comb(M, vector(M, 0)); for (int i = 0; i < M; i++) { for (int j = 0; j <= i; j++) { if (j == 0 || i == j) { Comb[i][j] = 1; } else { Comb[i][j] = Comb[i - 1][j] + Comb[i - 1][j - 1]; } } } int A, B, C, N; cin >> A >> B >> C >> N; dp[A][B][C][0] = 1; for (int a = A; a >= 0; a--) { for (int b = B; b >= 0; b--) { for (int c = C; c >= 0; c--) { for (int n = 0; n < N; n++) { // get 2 as if (a >= 2) { dp[a - 1][b][c][n + 1] += dp[a][b][c][n] * Comb[a][2] / Comb[a + b + c][2]; } // get 2 bs if (b >= 2) { dp[a][b - 1][c][n + 1] += dp[a][b][c][n] * Comb[b][2] / Comb[a + b + c][2]; } // get 2 cs if (c >= 2) { dp[a][b][c - 1][n + 1] += dp[a][b][c][n] * Comb[c][2] / Comb[a + b + c][2]; } // get a and b if (a >= 1 && b >= 1) { dp[a][b][c][n + 1] += dp[a][b][c][n] * a * b / Comb[a + b + c][2]; } // get b and c if (b >= 1 && c >= 1) { dp[a][b][c][n + 1] += dp[a][b][c][n] * b * c / Comb[a + b + c][2]; } // get a and c if (a >= 1 && c >= 1) { dp[a][b][c][n + 1] += dp[a][b][c][n] * a * c / Comb[a + b + c][2]; } } } } } double ans_a = 0, ans_b = 0, ans_c = 0; for (int a = 0; a <= A; a++) { for (int b = 0; b <= B; b++) { for (int c = 0; c <= C; c++) { ans_a += (A - a) * dp[a][b][c][N]; ans_b += (B - b) * dp[a][b][c][N]; ans_c += (C - c) * dp[a][b][c][N]; } } } cout << setprecision(10) << fixed << ans_a << ' ' << ans_b << ' ' << ans_c << '\n'; return 0; }