组合数计算：特定公式结果求解与概率分析

首先，我们需要计算组合数。组合数C(n, k)表示从n个元素中选择k个元素的方式数。 公式中的C(n, k)可以使用以下公式计算： C(n, k) = n! / (k! * (n-k)!) 其中，n!表示n的阶乘，即n! = n * (n-1) * (n-2) * ... * 2 * 1。 现在，我们来计算公式的结果： [C(5, 1) * C(1000, 4) + C(5, 2) * C(1000, 3) + C(5, 3) * C(1000, 2) + C(5, 4) * C(1000, 1)] / C(1005, 5) = [5! / (1! * (5-1)!) * 1000! / (4! * (1000-4)!) + 5! / (2! * (5-2)!) * 1000! / (3! * (1000-3)!) + 5! / (3! * (5-3)!) * 1000! / (2! * (1000-2)!) + 5! / (4! * (5-4)!) * 1000! / (1! * (1000-1)!)] / (1005! / (5! * (1005-5)!)) = [5 * 1000! / (4! * 996!) + 10 * 1000! / (3! * 997!) + 10 * 1000! / (2! * 998!) + 5 * 1000! / (1! * 999!)] / (1005! / (5! * 1000!)) = [5 * 1000 * 999 * 998 * 997 + 10 * 1000 * 999 * 998 + 10 * 1000 * 999 + 5 * 1000] / (1005 * 1004 * 1003 * 1002 * 1001 / (5 * 4 * 3 * 2 * 1)) = (5 * 1000 * 999 * 998 * 997 + 10 * 1000 * 999 * 998 + 10 * 1000 * 999 + 5 * 1000) / (1005 * 1004 * 1003 * 1002 * 1001 / 120) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) / (1005 * 1004 * 1003 * 1002 * 1001 / 120) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 * 999 * 998 * 997 + 10 * 999 * 998 + 10 * 999 + 5) * 120 / (1005 * 1004 * 1003 * 1002 * 1001) = (5 *