Can someone please explain this? How did that conclusion arrive?

P(Type I error) = P(reject H0 | H0 is true) = P(X1 ≤ c, X2 ≤ c | N = 16)

= cC2 / 16C2 = c(c-1)/240

What if it was

P(Type I error) = P(reject H0 | H0 is true) = P((X1+X2)/2 ≤ c | N = 16)

would the equation be different?