1st case:we have taken 1 pair.then from 8 pairs,we can choose it in 8 ways.now we have to take another 6 shoes from remaining 7 pairs, which will not be pair of anyone.this will be 7C6 * 26 =7*64=448(choosing 6 pairs from 7. after that taking any one of them from each pair).so total ways=(8*448)=3584
2nd case:we have taken 2 pairs.then from 8 pairs,we can choose it in 8C2=28 ways.now we have to take another 4 shoes from remaining 6 pairs, which will not be pair of anyone.this will be 6C4 * 24 =15*16=240(choosing 4 pairs from 6. after that taking any one of them from each pair).so total ways=(28*240)=6720
3rd case:we have taken 3 pairs.then from 8 pairs,we can choose it in 8C3=56 ways.now we have to take another 2 shoes from remaining 5 pairs, which will not be pair of anyone.this will be 5C2 * 22=10*4=40(choosing 2 pairs from 5. after that taking any one of them from each pair).so total ways=(56*40)=2240
so required probability=(3584+6720+2240)/16C8=6272/6435=0.9746