求解 50!/4!(50-4)!

$$\frac{ 50 ! }{ 4 ! (50-4) ! }$$

求值

$$230300$$

求解步骤

50 的阶乘是 30414093201713378043612608166064768844377641568960512000000000000。

$$\frac{30414093201713378043612608166064768844377641568960512000000000000}{4!\left(50-4\right)!}$$

4 的阶乘是 24。

$$\frac{30414093201713378043612608166064768844377641568960512000000000000}{24\left(50-4\right)!}$$

将 50 减去 4，得到 46。

$$\frac{30414093201713378043612608166064768844377641568960512000000000000}{24\times 46!}$$

46 的阶乘是 5502622159812088949850305428800254892961651752960000000000。

$$\frac{30414093201713378043612608166064768844377641568960512000000000000}{24\times 5502622159812088949850305428800254892961651752960000000000}$$

将 24 与 5502622159812088949850305428800254892961651752960000000000 相乘，得到 132062931835490134796407330291206117431079642071040000000000。

$$\frac{30414093201713378043612608166064768844377641568960512000000000000}{132062931835490134796407330291206117431079642071040000000000}$$

30414093201713378043612608166064768844377641568960512000000000000 除以 132062931835490134796407330291206117431079642071040000000000 得 230300。

$$230300$$

因式分解

$$2^{2}\times 5^{2}\times 7^{2}\times 47$$