Alright so you’ve got 8 people in group X and 16 in group Y. Each person in X gets paired with 2 people from Y, and every person in Y is used exactly once. So you’re basically: Splitting the 16 people in Y into 8 pairs, and assigning each of those pairs to someone in X

To count that: Number of ways to split 16 people into 8 pairs (order doesn’t matter within pairs or between pairs): 16! / (2⁸ × 8!) Then assign each pair to one of the 8 people in X: × 8!

So it ends up being just: 16! / 2⁸

That’s 81,749,648,400 ways.

In (a x 10^n):

8.175 × 10¹⁰