Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 4 - Probability and Counting Rules - 4-4 Counting Rules - Extending the Concepts - Page 237: 70


a. 4 b. $1020$ c. 13 d. $3744$

Work Step by Step

a. Royal flush 4 (AKQJ10, 4 types) b. Straight flush (not including a royal flush) each position have 4 choices, 5 cards, $4^5-4=1020$ c. Four of a kind 13 (AAAA, KKKK, etc ) d. Full house There are 13 choices for the three cards, the three cards come from a 4-card pool ($_4C_3=4$), total $13\times 4$ There are 12 choices for the pair which come from a 4-card pool ($_4C_2=6$), total $12\times 6$ Total for full house: $13\times 4\times12\times 6=3744$
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