Calculating Odds
I'm having a minor brain fail about this and thought someone here might be able to help?* So there are 2 decks of cards, one with 12 unique cards in and another with 16 unique decks of cards in.
These cards are then presented to the player five pairs at a time, where a pair is formed by drawing the top card from each deck. Player 1 may then select any pair, at which time, a new pair is drawn to replace the selected one and the second player is given a choice of which pair to pick. When the deck of 12 unique cards runs out, it is re-shuffled and pairs are drawn until the 16 card deck runs out.
The question is, how many unique possible games** exist? I'm utterly confused as to how to go about solving this? Help much appreciated! :)
*As some of you may already know, I'm not a student and therefore this is not a homework question.
**A game is players taking it turns to select pairs until all pairs have been selected.
These cards are then presented to the player five pairs at a time, where a pair is formed by drawing the top card from each deck. Player 1 may then select any pair, at which time, a new pair is drawn to replace the selected one and the second player is given a choice of which pair to pick. When the deck of 12 unique cards runs out, it is re-shuffled and pairs are drawn until the 16 card deck runs out.
The question is, how many unique possible games** exist? I'm utterly confused as to how to go about solving this? Help much appreciated! :)
*As some of you may already know, I'm not a student and therefore this is not a homework question.
**A game is players taking it turns to select pairs until all pairs have been selected.
Yeah, I was gonna say. How the hell do you even get those numbers? Black magic? o_O
I think its (12! * 16! / 4!) * 12P4 * 4! , but I'm not sure I understand the game exactly.
http://www.wolframalpha.com/input/?i=%2812!+*+16!+%2F+4!%29+*+%2812+permute+4%29+*+4!
http://www.wolframalpha.com/input/?i=%2812!+*+16!+%2F+4!%29+*+%2812+permute+4%29+*+4!
Oh, wait. There's an error, there.
12! - Permute one deck
16! - Permute the other deck
12P4 - Permute the first deck again and take only the top 4 cards.
5^16(16 - 4) - Choose 1 out of 5 pairs, repeat 12 times (after the first choice, there are 11 choices left, or 16 - 5).
12! - Permute one deck
16! - Permute the other deck
12P4 - Permute the first deck again and take only the top 4 cards.
5^
Okay I think I see.
So if the game was scaled up to have 7 pairs to choose from, it would be exactly the same, but 7 ^ (16-4)?
So if the game was scaled up to have 7 pairs to choose from, it would be exactly the same, but 7 ^ (16-4)?
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