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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Q: From a standard​ 52-card deck, how many 7​-card hands consist of 5 clubs and 2 diamonds​?

A: There are total 13 clubs and 13 diamonds.  We can pick 5 clubs from 13 clubs in 13C5 ways. We can…

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A: pick 9 numbers from 1 to 40. order doesn't matter. no. of ways to choose = ?

Q: How many different 4 card hands can be dealt from a deck of 52 cards?

A:

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Q: A student has 7 books on his deck. In how many different ways can he select a set of 3?

A: student has 7 books on his deck. No. of different ways to select set of 3 = ?

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Q: How many 13-card bridge hands can be chosen from a deck of cards

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Q: In a lottery game, a player picks 8 numbers from 1 to 49. How many different choices does the player…

A: From the provided information,The player has to pick 8 numbers from 1 to 49.

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

A:

Q: How many​ 5-card hands can be dealt from a standard deck of 52​ cards?

A: The objective of this question is to find out the number of different 5-card hands that can be dealt…

Q: A die is rolled six times and the order of the rolls is considered. In how many ways can three 2's,…

A: Given : A die is rolled six times and order is considered

Q: A standard card deck has 52 cards. How many thirteen-card hands are standard deck? possible from a

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Q: How many different 6 card hands can be dealt from a deck of 52 cards? Your answer is

A:

Q: how many hands of 33 cards can be made, where all cards are of the same suit?

A:

Q: How many 13-card hands having exactly 11 cards from any suit can be dealt? Please write out each…

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.