Probability

Total number of ways to choose 4 shoes from $8={}^{8}C_{4}=70$We want to choose 4 shoes that none of them form a pair.Firstly, choose 4 different pairs from the 4 available pairs $={}^{4}C_{4}=1$For each of the 4 pairs, 2 choices (left or right) $=2^{4}=16$.Hence, total number of ways to choose 4 shoes with no pair $=1 \times 2^{4}=16$.Thus, number of ways with atleast one pair $=70-16=54$.∴ Required probability $=\;\frac{54}{70}=\;\frac{27}{35}$