2 Answers

Person 1 can be matched with 7
Person 2 then matched with 6 (already matched with 1)
Person 3 then matched with 5 (already matched with 1 and 2) 
Person 4 then matched with 4 (already matched with 1, 2, and 3)
Person 5 then matched with 3 (already matched with 1, 2, 3, and 4)
Person 6 then matched with 2 (already matched with 1, 2, 3, 4, and 5)
Person 7 then matched with 1 (already matched with 1, 2, 3, 4, 5, and 6)
Person 8 has already been matched with everybody.

7 + 6 + 5 + 4 + 3 + 2 + 1 = 28

Then you can match Person 1 with 2 and 3, 2 and 4, 2 and 5, 2 and 6, 2 and 7, 2 and 8.
*  Follow through with Person 2 and similar matches
Then you can match Person 1 with 2, 3, 4, then 2, 3, 5, then 2, 3, 6, then 2, 3, 7, then 2, 3, 8.
Repeat from *
Then you can match Person 1 with 3 and 4, 3 and 5, 3 and 6, 3 and 7, 3 and 8.
Repeat from *
Then you can match Person 1 with 3, 4, 5; 3, 4, 6; 3, 4 7; 3, 4, 8.,
Repeat from *
Then you can match Person 1 with 4 and 5, 4 and 6, 4 and 7, 4 and 8
Repeat from *
Then you can match Person 1 with 4, 5, 6, and then 4, 5, and 7, then 4, 5, and 8..
Repeat from *
Then you can match Person 1 with 5 and 6, then 5 and 7, then 5 and 8
Repeat from *
Then you can match Person 1 with 5, 6, and 7 ; then 5, 6, and 8.
Repeat from *
NOW I am confused??? 

male and female?

old and young?

gay and straight?

Chinese and South African?

I'd say the number cannot be calculated ...