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In the game of poker played with an ordinary deck of 52 cards various five-card holdings are given special names. The name "three of a kind" is reserved for a holding that meets the following rule: Three cards of the same denomination and two other cards of different denominations. The number of distinct "three of a kind" that can be drawn from a 52-card deck can be calculated with the following product expression: 000¹ Explain what each of the factors in the expression represents in terms of selections from the deck of cards. Follow the examples given in slides 8-10 of the lecture Section 9.5 Combinations.pdf.

In the game of poker played with an ordinary deck of 52 cards various five-card holdings are given special names. The name "three of a kind" is reserved for a holding that meets the following rule: Three cards of the same denomination and two other cards of different denominations. The number of distinct "three of a kind" that can be drawn from a 52-card deck can be calculated with the following product expression: 000¹ Explain what each of the factors in the expression represents in terms of selections from the deck of cards. Follow the examples given in slides 8-10 of the lecture Section 9.5 Combinations.pdf.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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In the game of poker played with an ordinary deck of 52 cards various five-card holdings are given special names. The name "three of a kind" is reserved for a holding that meets the following rule: Three cards of the same denomination and two other cards of different denominations. The number of distinct "three of a kind" that can be drawn from a 52-card deck can be calculated with the following product expression: 030² Explain what each of the factors in the expression represents in terms of selections from the deck of cards. Follow the examples given in slides 8-10 of the lecture Section 9.5 Combinations.pdf.
Transcribed Image Text:In the game of poker played with an ordinary deck of 52 cards various five-card holdings are given special names. The name "three of a kind" is reserved for a holding that meets the following rule: Three cards of the same denomination and two other cards of different denominations. The number of distinct "three of a kind" that can be drawn from a 52-card deck can be calculated with the following product expression: 030² Explain what each of the factors in the expression represents in terms of selections from the deck of cards. Follow the examples given in slides 8-10 of the lecture Section 9.5 Combinations.pdf.
SLIDES: - Four of a kind - Full house - Flush What are we choosing? Your turn (¹3) (3) (4) (49) (4) Straight 4 cards one denomination with free fifth card (¹9) (4) ³ (19)) 3 cards one denomination 2 cards another denomination ()(4) - Straight flush Denomination for three cards Suit for three cards Choose Choose fifth card denomination denomination and suit Suit for two cards Named Hands of Cards 3 Denomination for two cards 5 cards same suit Not straight or royal flush (0) Choose five cards in a suit Choose the suit 5 adjacent denominations Not all same suit Subtract Choose starting denomination of straight straight or Choose suit royal flush 30-40 (9)0³-(90) Choose starting denomination of straight Choose a suit for each of five cards 5 in order, same suit, not royal flush, Ace H/L Choose starting denomination of straight Choose one suit for all five cards Example 9.5.9 Poker Hand Problems in Epp on page 626 In the card game poker, various 5-card hands have names - The number of ways to select a named hand creates its probability of being dealt at random - The named hands are ordered by probability of selection - Lower probability hand beats higher probability hands in the game - Royal flush 10,J,K,Q,A of same suit Subtract straights of same suit Count = - ©* Choose 10, J, K, Q, A in one suit 10 cards can start the straight Choose one of four suits Subtract four royal flushes Choose one of four suits (99-0
Transcribed Image Text:SLIDES: - Four of a kind - Full house - Flush What are we choosing? Your turn (¹3) (3) (4) (49) (4) Straight 4 cards one denomination with free fifth card (¹9) (4) ³ (19)) 3 cards one denomination 2 cards another denomination ()(4) - Straight flush Denomination for three cards Suit for three cards Choose Choose fifth card denomination denomination and suit Suit for two cards Named Hands of Cards 3 Denomination for two cards 5 cards same suit Not straight or royal flush (0) Choose five cards in a suit Choose the suit 5 adjacent denominations Not all same suit Subtract Choose starting denomination of straight straight or Choose suit royal flush 30-40 (9)0³-(90) Choose starting denomination of straight Choose a suit for each of five cards 5 in order, same suit, not royal flush, Ace H/L Choose starting denomination of straight Choose one suit for all five cards Example 9.5.9 Poker Hand Problems in Epp on page 626 In the card game poker, various 5-card hands have names - The number of ways to select a named hand creates its probability of being dealt at random - The named hands are ordered by probability of selection - Lower probability hand beats higher probability hands in the game - Royal flush 10,J,K,Q,A of same suit Subtract straights of same suit Count = - ©* Choose 10, J, K, Q, A in one suit 10 cards can start the straight Choose one of four suits Subtract four royal flushes Choose one of four suits (99-0
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