Question

How many subsets contain exactly one even number?

a) 2ⁿ⁻¹
b) n/2
c) n - 1
d) 2ⁿ⁻¹

Answer 1

The number of subsets with exactly one even number is 2^(n-1).

Step-by-step explanation:

The number of subsets that contain exactly one even number can be calculated using the formula 2^(n-1), where n is the number of elements in the set. Let's say we have a set with n elements. To form a subset with exactly one even number, we can select one of the even numbers (which is 2^(n-1)) and then select the remaining odd numbers from the remaining (n-1) elements. Therefore, the correct answer is option a) 2^(n-1).