10 pairs of shoes(ie 20 shoes) pick 8.

P(no complete pair)

P(exactly 1 complete pair)

P(exactly 1 complete pair)= 10C1(pick the pair) *18C1*16C1*14C1*12C1*.../20C8

i dont know why this doesnt work? im picking a pair then picking each other shoe such that i dont pick its pair...?

P(no complete pair)= 1-P(at least 1 complete pair)

which i would do in the same fashion as above but its not working so im missing something.