What is my error ?

I played in a PS tournament and two players went all in on the flop against my top pair ace kicker.

They had 6 and nine outs. (Flush draw and open straight draw with the flush cards no good for the straight draw)

I think, the probability of me winning when they combined have 15 outs is 46% (32/47*31/46)

But if I try another way, I dont get the same result :

Probability of the 6 outs beating me 1-(41/47*40/46) = 24%

Probability of the 9 outs beating me when the 6 outs havent beated me (1-0,24)*(1-(38/47*37/46) = 27%

If I add those two I get 51%

You could say that it doesnt matter very much as I am getting around 1:1 odds with the pot laying 2:1, but it has been obsessing me.

By the way, I won this hand and later lucked out to win the tournament.

Kim