501
The number of ways of selecting n out of m is m!/(n!m!). So let's do that for selecting 2, 3, 4, 5, 6, 7, and 8 out of 10.
2!/(2!8!) = 45
3!/(3!7!) = 120
4!/(4!6!) = 210
5!/(5!5!) = 252
6!/(6!4!) = 210
7!/(7!3!) = 120
8!/(8!2!) = 45
Now add them all together.
45 + 120 + 210 + 252 + 210 + 120 + 45 = 1002
But you're not quite done. It there really any difference between having a group with persons AB and the 2nd group being CDEFGHIJ or the first group being CDEFGHIJ and the 2nd group AB? The answer is no, so you need to divide the number above by 2, giving
1002 / 2 = 501
So there are 501 to separate 10 people into 2 groups with each group having at least 2 people.
