Can you use combinations?
Yes, you can. 10C1/20C2=1/19 The 10C1 part is for the number of ways you can pick a pair of matching shoes from ten possible pairs, which is just 10. 20C2 is for the number of ways you can pick any two shoes from 20 shoes, which is 190. So the probability of picking matching shoes is this: the number of ways you can pick a matching pair divided by the total number of ways you can pick any two shoes.