2) (a) Recall that a standard deck of cards has 52 cards, consisting of 13 ranks with four suits each. Suppose that you combine two identical standard decks into one superdeck of 104 cards. Count the number of distinct ten-card hands that can be drawn from this superdeck of cards. Define a fuller house to be a ten-card hand with five cards of the same rank, three cards of a different rank, and two cards of another rank. Count the number of ten-card hands that are fuller houses. Note: One cxample of a fuller house is thc hand 44 4% 4♡ 40 40 K♡ K$ K$ A♡ AO.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 74E: Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is...
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(Q2) (a) Recall that a standard deck of cards has 52 cards, consisting of 13 ranks with four suits each.
Suppose that you combine two identical standard decks into one superdeck of 104 cards.
Count the number of distinct ten-card hands that can be drawn from this superdeck of cards.
Define a fuller house to be a ten-card hand with five cards of the same rank, three cards of a
different rank, and two cards of another rank. Count the number of ten-card hands that are
fuller houses.
Note: One example of a fuller house is the hand
44 4 4♡ 40 40 K♡ K$ K$ A♡ AO.
Transcribed Image Text:(Q2) (a) Recall that a standard deck of cards has 52 cards, consisting of 13 ranks with four suits each. Suppose that you combine two identical standard decks into one superdeck of 104 cards. Count the number of distinct ten-card hands that can be drawn from this superdeck of cards. Define a fuller house to be a ten-card hand with five cards of the same rank, three cards of a different rank, and two cards of another rank. Count the number of ten-card hands that are fuller houses. Note: One example of a fuller house is the hand 44 4 4♡ 40 40 K♡ K$ K$ A♡ AO.
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