A standard deck of cards has 52 cards. There are four suits: ♥, ♦, ♣, ♠. For each suit, there are thirteen denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. Here are all the cards: 2♥, 3♥, 4♥, 5♥, 6♥, 7♥, 8♥, 9♥, 10♥, J♥, Q♥, K♥, A♥ 2♦, 3♦, 4♦, 5♦, 6♦, 7♦, 8♦, 9♦, 10♦, J♦, Q♦, K♦, A♦ 2♣, 3♣, 4♣, 5♣, 6♣, 7♣, 8♣, 9♣, 10♣, J♣, Q♣, K♣, A♣ 2♠, 3♠, 4♠, 5♠, 6♠, 7♠, 8♠, 9♠, 10♠, J♠, Q♠, K♠, A♠ Six cards are called a tremendous hand if they can be split into two disjoint groups satisfying the following conditions: • The first group has three cards of the same denomination. • The second group has three cards of the same suit. How many tremendous hands are there
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.
A standard deck of cards has 52 cards. There are four suits: ♥, ♦, ♣, ♠. For each suit, there are thirteen
denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. Here are all the cards:
2♥, 3♥, 4♥, 5♥, 6♥, 7♥, 8♥, 9♥, 10♥, J♥, Q♥, K♥, A♥
2♦, 3♦, 4♦, 5♦, 6♦, 7♦, 8♦, 9♦, 10♦, J♦, Q♦, K♦, A♦
2♣, 3♣, 4♣, 5♣, 6♣, 7♣, 8♣, 9♣, 10♣, J♣, Q♣, K♣, A♣
2♠, 3♠, 4♠, 5♠, 6♠, 7♠, 8♠, 9♠, 10♠, J♠, Q♠, K♠, A♠
Six cards are called a tremendous hand
if they can be split into two disjoint groups satisfying the following
conditions:
• The first group has three cards of the same denomination.
• The second group has three cards of the same suit.
How many tremendous hands are there?
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