What Are the Odds of Drawing at Least One King, Queen, or Ace in Three Attempts?

[clarkd25]

In a 52 card deck if you choose 3 random cards such as any King any queen or any ace
(12 cards in total) what is the probability of being able to draw at least one of these cards with 3 attempts and not replacing a drawn card. Basically my question is regarding the odds in Texas Holdem of choosing 3 random cards and flopping at least one of them. It seems to me that on the first card the odds of success are 12/52 and then on the second draw if not successful would be 12/51 and then 12/50, but I just don't think I know how to do the math for the problem. Please Help.

 

[clarkd25]

Duh!

I went about solving the problem the wrong way. Instead of trying to figure out the probability of flopping at least one of the cards I should have solved for the probability of flopping none of the cards which would be (40/52)*(39/51)*(38/50) which results in 44.7%. This would mean that the probability of flopping at least one of my randomly selected cards woul be 55.3%. My reason for figuring out this problem is that I like to make prop bets when I play poker and wanted to know if this was a good even money bet for me to select 3 cards and betting that one of them would come on the flop. By having chance greater than 50% of hitting one of my cards this bet has a +EV.