A closet contains 10 pairs of shoes. if 8 shoes are randomly selected, what is the probability that there will be

There are 10 pairs of shoes. 8 shoes are select.

P = (2/20) (2/19) (2/18) (2/17) (2/16) (2/15) (2/14) (2/13)

P = 2^8 / (20P8)

But, any 8 differents shoes can be chosen from 10 pairs.

so there are 10C8 = 45 ways to do so

P = 45 * 2^8 / (20C8)

But, since order does not matter, there are 8! way you can select the 8 different shoes

P = 8! * 45 * 2^8 / (20C8)

P = 384/4199 or about 9.145%