Three Card Probability Question

Greetings!

If someone would be kind enough to verify this, I'd really appreciate it.

I'm determining the probability of an Ace-High hand with three cards dealt, but I don't want those that include Pairs, Straights, Trips or Flushes:

Ace High (Discludes Pairs/3OaK):

(4/52 * 48/51 * 47/50) * 3 = 0.20416289592760184

Okay, since 3Oak and Paired Aces are automatically out of that, I just need to subtract out Flushes, Straights and other Pairs:

Less All Flushes, Including Straight Flush:

0.20416289592760184 - ((4/52 * 12/51 * 11/50) * 3) = 0.19221719457013578

Now we carry the result:

Straights w/Ace less Straight Flushes:

((4/52 * 8/51 * 7/50) - (4/52 * 2/51 * 1/50)) * 3 = 0.004886877828054299

0.19221719457013578 - 0.004886877828054299 = 0.18733031674208148

Now we carry the result:

Less Any Other Pair:

0.18733031674208148 - ((4/52 * 48/51 * 3/50) *3) = 0.17429864253393668

Result

The probability of having an Ace-High with no hand that is a pair or better is 0.17429864253393668.

Sound right?

Type =4*(combin(12,2)-2)*15/combin(52,3) in excel. No computer here or I would.
4 aces
Choose 2 of 12 ranks for the other 2 cards minus the 2 ways to make a straight.
15 suits combinations for the 2 cards.

Quote: miplet

Type =4*(combin(12,2)-2)*15/combin(52,3) in excel. No computer here or I would.
4 aces
Choose 2 of 12 ranks for the other 2 cards minus the 2 ways to make a straight.
15 suits combinations for the 2 cards.

Thanks, Miplet!

0.173755656 is the result.

I was close, don't know what I did wrong.

^^^

Yep, that's right. Leading to 3840/22100 = 0.1737556561

You double counted somewhere Mission.

I didn't subtract something that I should have, or had a formula wrong.

Quote: Mission146

I didn't subtract something that I should have, or had a formula wrong.

Straights (Ace-high AND Ace-low: changes in bold) minus straight flushes:

((4/52 * 8/51 * 4/50) - (4/52 * 2/51 * 1/50)) * 3 * 2 = 0.005429864

Quote:

Straights w/Ace less Straight Flushes:

((4/52 * 8/51 * 7/50) - (4/52 * 2/51 * 1/50)) * 3 = 0.004886877828054299

Should be:

(4/52 * 16/51 * 4/50) - (4/52 * 4/51 * 1/50)) * 3= ???

A23 and AKQ are both straights.

Edit: yep typing on phone is slow. :+)

Thanks again!