Probability

Total number of ways to choose 4 shoes from 8=‌8C4=70
We want to choose 4 shoes that none of them form a pair.
Firstly, choose 4 different pairs from the 4 available pairs =‌4C4=1
For each of the 4 pairs, 2 choices (left or right) =24=16.
Hence, total number of ways to choose 4 shoes with no pair =1×24=16.
Thus, number of ways with atleast one pair =70−16=54.
∴ Required probability =‌

54

70

=‌

27

35