关于组合的问题

Question

这是任务

How many ways are there to choose from the set {1, 2, . . . , 100} three distinct
numbers so that their sum is even?

首先，即使只有

，三个数字之和也是如此

1.all number is even
2.two of them is odd and one is even

我知道

(n)   =  n!/(k!*(n-k)!   
(k)   

任何人都可以帮我解决这个问题

Answer 1

那不就是

(50 choose 3) + (50 choose 2) * (50 choose 1)