Question

In how many ways can two integers be selected from 60 consecutive positive integers so that their sum is even?

Answer 1

Using the combination formula, it is found that the integers can be chosen in 870 ways.

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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:

$T = 2C_{30,2} = 2\frac{30!}{2!28!} = 870$

The integers can be chosen in 870 ways.

You can learn more about the combination formula at brainly.com/question/25821700