A standard 5- card poker hand is drawn simultaneously from a deck of 52 cards. You draw a “flush” if all 5 cards are the same suit. Answer the following questions: 1. How many ways can you get a flush with all hearts? 2. How many ways can you get a flush with any suit?
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.
Given: A standard 5- card poker hand is drawn simultaneously from a deck of 52 cards. You draw a “flush” if all 5 cards are the same suit.
1. To get a flush with all hearts, it required to draw the 5 cards from 13 heart cards of a deck.
Therefore the number of ways of drawing 5 cards from 13 cards is: ways.
Thus there are 1287 ways of drawing a flush with all hearts.
2. Flush with any suit can be in the following cases:
(i) Flush with Clubs
(ii) Flush with Diamonds
(iii) Flush with Hearts
(iv) Flush with spades
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