题目链接 隐隐约约记得展开式和组合数的关系，但是记不起来，百度了才知道二项式定理。 ( x + y ) n = C ( n , 0 ) × x n × y 0 + C ( n , 1 ) × x n − 1 × y 1 + C ( n , 2 ) × x n − 2 × y 2 . . . . . . + C ( n , n ) × x 0 × y n (x+y)^n=C(n,0)\times x^n \times y^0+C(n,1)\times x^{n-1} \times y^1+C(n,2)\times x^{n-2} \times y^2......+C(n,n)\times x^0 \times y^n (x+y)n=C(n,0)×xn×y0+C(n,1)×xn−1×y1+C(n,2)×xn−2×y2......+C(n,n)×x0×yn 知道二项式定理之后就是一个裸题了 答案就是 C ( k , n ) × a n × b m C(k,n)\times a^n\times b^m C(k,n)×an×bm
AC代码：
/* * @Author: hesorchen * @Date: 2020-04-14 10:33:26 * @LastEditTime: 2020-06-30 22:12:29 * @Link: https://hesorchen.github.io/ */ #include <map> #include <set> #include <list> #include <queue> #include <deque> #include <cmath> #include <stack> #include <vector> #include <cstdio> #include <string> #include <cstdlib> #include <cstring> #include <iostream> #include <algorithm> using namespace std; #define endl '\n' #define PI acos(-1) #define PB push_back #define ll long long #define INF 0x3f3f3f3f #define mod 10007 #define pll pair<ll, ll> #define lowbit(abcd) (abcd & (-abcd)) #define max(a, b) ((a > b) ? (a) : (b)) #define min(a, b) ((a < b) ? (a) : (b)) #define IOS \ ios::sync_with_stdio(false); \ cin.tie(0); \ cout.tie(0); #define FRE \ { \ freopen("in.txt", "r", stdin); \ freopen("out.txt", "w", stdout); \ } inline ll read() { ll x = 0, f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + (ch ^ 48); ch = getchar(); } return x * f; } //============================================================================== ll quick_pow(ll a, ll b) { ll res = 1; while (b) { if (b & 1) res = res * a % mod; a = a * a % mod; b /= 2; } return res % mod; } ll jc[2500]; void init() { jc[0] = 1; for (int i = 1; i < 2345; i++) jc[i] = jc[i - 1] * i % mod; } ll C(ll n, ll m) { ll a = n % mod; ll b = m % mod; if (a < b) return 0; if (a && b) return jc[a] * quick_pow(jc[b], mod - 2) % mod * quick_pow(jc[a - b], mod - 2) % mod * C(n / mod, m / mod) % mod; else return 1; } int main() { ll a, b, k, n, m; cin >> a >> b >> k >> n >> m; init(); cout << C(k, n) * quick_pow(a, n) * quick_pow(b, m) % mod << endl; return 0; } /* */