The Theory of Poker - Newbie

[Maximus]

I am reading The Theory of Poker and am trying to understand how he gets the calculations done in Chapter 5, pages 38 to 41. For example, playing 7-stud, you start with 3 spades and have seen seven other cards. The following table shows the effect of the other cards on making the flush.

Number of Spades / Chances of Flush %
0 / 23.6%
1 / 19.6%
2 / 15.8%
3 / 12.3%
4 / 9.1%

I do not understand how this is determined.
I tried myself using this equation:
52 cards minus 3 I have minus 7 on the table. That gives me 42 remaining cards. There are 11 cards I can get to get the flush, thus 31 cards that can beat me. That means I have a 31 to 11 chance of getting a spade. However, that does not equal 23.6% (rather 35%). Obviously, I am not understanding how to calculate this. Any help would be GREATLY appreciated!

Thanks!