Trio
Full houses are called by the cards they consist of. For instance a Full House KKKTT is a full house Kings over Tens. In the case of TTTKK its a full house Tens over kings. So basically its a full house [The three of a kind] over [the pair].
There are 4 tens, 4 jacks, and 52 total cards. Assuming you take a single card out of a full and shuffled deck, the chances are 8/52=2/13=15.38%.
When the deck is full, this probability is 4/52 (the probability of getting one of 4 aces) times 16/51 (the probability of getting one of 16 kings, queens, jacks, or tens) times 2 (the number of orders in which you could get these cards: ace first, or ace second). This comes out to 32/663, or about 4.83%. Of course, this probability changes as the game progresses: it decreases when any of the tens, jacks, queens, kings, or aces get discarded, but increases when other cards get discarded. This change is unpredictable, but its expected value is 0; this is a complicated concept to explain, but it means that on average, the probability will go up as much as it goes down. Also, the probability is still 32/663 at any point in the game if you have no information whatsoever about what cards came up before: if you forgot every card you saw, or if you just joined the game.
To find out how many tens are in 485, you divide 485 by 10. This gives you 48.5, which means there are 48 full tens in 485. Therefore, there are 48 tens in 485.
The probability of drawing two jacks and three tens of any suite from a standard deck of cards is: 5C2 ∙ (4/52)∙(3/51)∙(4/50)∙(3/49)∙(2/48) = 0.00000923446... ≈ 0.0009234% where 5C2 = 5!/[(5-2)!∙(2!)] = 10
The pair of queens beat the pair of tens, the nine and the ace are irrelevant. Queens are higher ranked than tens.
In an ordinary deck of cards here are four of every denomination -- one in every suit (one in hearts, one in spades, etc.) There are four aces, four two's, four tens, four jacks and on and on.
In the game of pinochle, players earn points based on the cards they capture in tricks during the game. Aces and tens are worth 10 points each, while kings, queens, jacks, and nines are worth 5 points each. The team that reaches a predetermined point total first wins the game.
In Pinochle, the points are calculated based on the cards in your hand. Aces are worth 11 points, tens are worth 10 points, kings are worth 4 points, queens are worth 3 points, jacks are worth 2 points, and nines are worth 0 points. The total points in a hand are added up to determine the score for that hand.
The 10s and 5s
A standard 52 cards deck contains 4 kings and 4 tens. Given that the type of the card does not matter, we have a total of 8 valid cards (4 kings + 4 tens) to choose from a 52 cards deck. Hence the probability is 8/52.