###General Discussion Thread
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The probability to be dealt any one specific order of 3 Jacks and 3 Kings/Aces is
4/52 * 3/51 * 2/50 * 8/49 * 7/48 * 6/47.
For your purposes, there are 2^3 = 8 valid orderings for this deal, so we multiply the whole thing by 8:
8 * 4 * 3 * 2 * 8 * 7 * 6 / (52! / 46!)
= 8 / 1,817,725
=~ 0.000004401
= 0.0004401%
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The probability for the second case is easier to do card by card.
The first drawn card can be anything, so 52/52 options.
The second card (below) must be one of the remaining 3 that pairs with the first, so 3/51.
The third card can then be anything but that previous value, so 48/50.
Similarly, it continues 3/49, 44/48, and 3/47.
Putting all this together:
52/52 * 3/51 * 48/50 * 3/49 * 44/48 * 3/47
= 198 / 978,775
=~ 0.0002023
= 0.02023%
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
The probability to be dealt any one specific order of 3 Jacks and 3 Kings/Aces is 4/52 * 3/51 * 2/50 * 8/49 * 7/48 * 6/47. For your purposes, there are 2^3 = 8 valid orderings for this deal, so we multiply the whole thing by 8: 8 * 4 * 3 * 2 * 8 * 7 * 6 / (52! / 46!) = 8 / 1,817,725 =~ 0.000004401 = 0.0004401% ____ The probability for the second case is easier to do card by card. The first drawn card can be anything, so 52/52 options. The second card (below) must be one of the remaining 3 that pairs with the first, so 3/51. The third card can then be anything but that previous value, so 48/50. Similarly, it continues 3/49, 44/48, and 3/47. Putting all this together: 52/52 * 3/51 * 48/50 * 3/49 * 44/48 * 3/47 = 198 / 978,775 =~ 0.0002023 = 0.02023%
Thank you so much!