Final answer:
Out of the possible combinations on the spinner, there are 3 outcomes where the sum is less than 7 and at least one number is even: (2,2), (2,4), and (4,2).
Step-by-step explanation:
The question requires us to find the number of outcomes where the sum of two spins on a spinner is less than 7 and at least one of the numbers is even. Since the spinner has numbers 2, 4, 5, and 7, the possible outcomes are (2,2), (2,4), (2,5), (2,7), (4,2), (4,4), (4,5), (4,7), (5,2), (5,4), (5,5), (5,7), (7,2), (7,4), (7,5), and (7,7).
To satisfy both conditions, we look for combinations that sum to less than 7 and include an even number. These are: (2,2), (2,4), and (4,2). Therefore, there are 3 outcomes with a sum less than 7 that contain at least one even number.