Question

in a game of poker, five players are each dealt 5 cards from a 52-card deck. how many ways are there to deal the cards?

Answer 1

The number of ways to deal 5 cards to 5 players from a 52-card deck in a game of poker is (52!)/[(27!)*(5!)^5].

• Permutations and combinations define nCr as ways of selecting 'r' number of items from 'n' items. 
• nCr = (n!)/[r!(n-r)!]
• here we want to deal 5 playing cards to each player.once we deal 5 playing cards to any participant,
• the playing cards left inside the deck are reduced through five.
• We deal a total of 25 playing cards, i.e., 5 playing cards to 5 gamers.
• The number of ways to deal five playing cards to the primary participant is 52C5.The number of approaches to deal 5 playing cards to the second one participant is 47C5.
• The wide variety of ways to deal 5 cards to the 0.33 player is 42C5.
• The variety of methods to deal 5 cards to the fourth participant is 37C5.
• The quantity of ways to deal 5 playing cards to the 5th player is 32C5.
• the full quantity of methods is the general multiplication.
• The total number of solutions = 52C5 * 47C5 * 42C5 * 37C5 * 32C5
• When we simplify, we get (52!)/[(27!)*(5!)^5]. 

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