A duelist playing the "Yu Gi Oh" trading card game wants to win using the Exodia cards. These are a set of five different cards, each containing a piece of Exodia's body. In the game, each player draws a starting hand of five cards. Assuming the player has a deck of 40 cards which contains a complete Exodia set and where all the cards are different (i.e. contains no duplicate cards), what are the odds that their starting hand of five cards will be the complete Exodia set?
Visitor 1550041760 posted an answer
9 months, 23 days ago
Answer: 1 / 658,008
Since all 40 cards are different and order does not matter, we must choose 5 cards out of 40. We use the formula 40! / (35! * 5!) to give us the number of combinations. (n! means n*(n-1)*(n-2)*...*3*2*1.) This gives (40*39*38*37*36) / (5*4*3*2*1), which gives 658,008 combinations. There is only one combination that consists of all five pieces of Exodia, so the odds of starting off with it are 1 / 658,008.
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