probability

Question

A closet contains 10 pairs of shoes. If 8 shoes
are randomly selected, what is the probability that
there will be exactly 1 complete pair?

ANSWER I AM GETTING : [ C(10,1) * C(9,6) * 2^6 ] / [ C(20,8) ]
ANSWER GIVEN               : [ C(10,1) * C(9,6) * 2^6 ] / [C[20,8] *2!]

PLEASE VERIFY IF AM MISSING SOMETHING

Answer 1

Your answer is correct.

Select 1 (i.e. 2 shoes) pair out of 10 pairs = 10C1

Remaining 6 different shoes out of 9 pairs = 9C6 * (Possible number of shoes from each of the 6 pair, which is $2^6$)

So P = $\frac{10C1 * 9C6 * 2^6}{20C8}$

I don't see any reason to divide by 2!

Comments

We don't need to know which  shoe from a pair is selected(left or right). I think that's why we divide by 2!, to remove those orders.