Using the combination formula, it is found that the integers can be chosen in 870 ways.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The resulting sum will be even if both numbers are even(2 from a set of 30) or if both numbers are odd(also 2 from a set of 30), hence:
[tex]T = 2C_{30,2} = 2\frac{30!}{2!28!} = 870[/tex]
The integers can be chosen in 870 ways.
You can learn more about the combination formula at https://brainly.com/question/25821700
