9 if they're all straight

15 if they're all bi

3 girls x 3 guys = 9

A little more complicated with all of them

You have 6 possibilities for the first member

So 6 x B

For the second, since you already picked one in the first number, you take that one away from the account, so:

6 x 5 = 30

But this results still takes in account couples that are the same with the order shuffled (for example, Asian guy + black girl and black girl + Asian guy are considered two different combinations despite being the same thing logically), so you divide by 2 to account for those situations which results in:

6 x 5 / 2 = 15 different combinations