in a standard deck of cards there are 52 cards each of which has a suit and a face value. Possible face values are ?,2,3,4,5,6,7,8,9,10,?,?,?A,2,3,4,5,6,7,8,9,10,J,Q,K and possible suits are ♢,♡,♣,♠♢,♡,♣,♠. Any combination of suit and face value makes a card. Part 1. How many ways are there to distribute the cards to 4 players, so that each player has 13 cards? Prove that if you distribute the cards as in part (1), then one of the players has at least 4 cards with a ♡♡.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Recall that in a standard deck of cards there are 52 cards each of which has a suit and a face value. Possible face values are ?,2,3,4,5,6,7,8,9,10,?,?,?A,2,3,4,5,6,7,8,9,10,J,Q,K and possible suits are ♢,♡,♣,♠♢,♡,♣,♠. Any combination of suit and face value makes a card.
Part 1. How many ways are there to distribute the cards to 4 players, so that each player has 13 cards?
Prove that if you distribute the cards as in part (1), then one of the players has at least 4 cards with a ♡♡.
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