[BruceZ]

Here are the solutions for all the cases.

There are 42 unseen cards containing 6-10 spades. You must draw at least 2 spades out of your remaining 4 cards to make a flush. It is easiest to add the probabilities of drawing 0 or 1 spade and subtract this from 1.

0 spades out, 10 spades in deck:

1 - [ C(32,4) + C(32,3)*10 ]/C(42,4) = 23.6%

C(32,4) is the number of ways to draw 0 spades, and C(32,3)*10 is the number of ways to draw 3 non-spades and 1 spade. C(42,4) is the number of ways to draw 4 cards out of 42. The others are done the same way.

1 spades out, 9 spades in deck:

1 - [ C(33,4) + C(33,3)*9 ]/C(42,4) = 19.6%

2 spades out, 8 spades in deck:

1 - [ C(34,4) + C(34,3)*8 ]/C(42,4) = 15.8%

3 spades out, 7 spades in deck:

1 - [ C(35,4) + C(35,3)*7 ]/C(42,4) = 12.3%

4 spades out, 6 spades in deck:

1 - [ C(36,4) + C(36,3)*6 ]/C(42,4) = 9.1%