I'm not sure I understand the question exactly, but here's my understanding: There are 100! ways to take them out one-at-a-time. There are 100 C 10 ways to choose the first ten, then of the remaining 90 there are 90! ways to choose those. Using this logic throughout, we would get 100! + (100 C 10)*90! + (100 C 20)*80! + ... + (100 C 90)*10!.
Hope this is the right way to understand the problem.
[Edit: Actually, rather than adding these we should probably multiply them since a difference in the way of doing the first selection constitutes a different overall process of selection.]