Final answer:
To calculate the number of ways to deal 13 cards to each of four players from a standard deck, use combinations: the product of 52C13, 39C13, and 26C13 for the first three players, with the fourth player receiving the remaining cards.
Step-by-step explanation:
The number of ways to deal hands from a standard playing deck of 52 cards to four players with each player getting exactly 13 cards can be calculated using combinations. Since the order of players does not matter, we are looking for the number of combinations of 52 cards taken 13 at a time. This can be denoted as 52C13. After the first player receives their 13 cards, there are 39 cards left. The second player's hand can be selected in 39C13 ways. Continuing this pattern, after the second player, there are 26 cards left for the third player, leading to 26C13 ways. Lastly, the fourth player would receive the remaining 13 cards, and thus there is only 1 way for this to occur.
The formula for a combination is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose. Therefore, the total number of ways to deal the cards is 52C13 * 39C13 * 26C13 * 1, factoring in that the first player can get any of the available cards, the second player can get any of the remaining, and so on.
To answer the original question succinctly, the number of ways to deal hands from a deck of cards to four players with each receiving 13 cards is the product of the combinations for each player's hand: 52C13 * 39C13 * 26C13.