My sock drawer has the following socks: 3 green, 5 white, and 7 black. I hurriedly pack for a trip one dark morning, randomly grabbing 5 socks from the drawer and putting them in the suitcase. What is the probability that I will have at least one pair of black socks?

Looking at this problem from a novice point of view, I thought that this would be simply $100\%$ minus the probability of choosing a set with no black socks. This, however, isn't the correct answer because the problem states the word 'pairs' which most likely affected the result.

How does this change my approach? What type of approach would you use instead "negating" the probability.