A poker hand consists of 5 cards from a standard deck of 52. Find the number of different poker hands of the specified type. **two pairs with exactly one pair being aces (two aces, two of another denomination, and one of a third)**

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A:

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A: Total number of cards is 52. The number of cards for the poker hand is 5.

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Q: If A = {1, 2, 3, 4, 5}, B = {1, 3, 4, 6}, C = {1, 6, 7}.

A:

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A: Given, How many 13-card hands having exactly 11 cards from any suit can be dealt?

Q: How many 5-card hands can be chosen from a deck of cards?

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.