Final answer:
To find the number of possible two pair hands for a friend in poker, considering the cards already held by another player, we calculate the combination of ranks and suits available for the two pairs and the number of viable kickers, then multiply these figures together.
Step-by-step explanation:
The question involves determining the number of ways a friend could be dealt a two pair in a 5-card poker hand from a standard deck, excluding the cards you have been dealt. We already know your hand, which includes Jacks of clovers (clubs), hearts, and spades, and unrelated cards 5 of diamonds and 8 of clubs. Since two pairs mean exactly two distinct ranks, and you hold three Jacks, your friend cannot have Jacks for their pairs. There are 12 remaining ranks and your friend needs two different ranks from these remaining ones. For the first pair, there are 12 options for the rank and 6 ways to choose 2 of the 4 suits. For the second pair, there are 11 remaining ranks and the same 6 potential combinations of suits. Lastly, the fifth card (kicker) must be of a rank different from the two pairs, and from the 44 remaining cards (52 total - 8 cards accounted for in the pairs and your hand), there are 40 cards that can serve as a kicker since it cannot match any of the two pair ranks nor the ranks in your hand. Thus, we calculate as follows:
Total ways to get two pairs = 12 (first pair rank options) × 6 (first pair suit combinations) × 11 (second pair rank options) × 6 (second pair suit combinations) × 40 (kicker options)
This will give the total number of ways the friend can receive a two pair hand given the constraints.