The correct option is D 20C1×(38C2−19)40C4
Out of 20 pairs, we need to select 1 pair and the other 2 shoes should not form a pair.
Thus, this can be achieved in: 201C∗(192C∗21C∗21C)
(i.e. select one pair, then out of the remaining 19 pairs, select 2 pairs and from each pair select one shoe)
We can also say that: select one pair, then out of the remaining 38 shoes, select 2 shoes and eliminate the 19 cases where these 2 shoes form a pair, i.e. 201C∗(382C−19)
Therefore, probability =201C∗(382C−19)404C