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Answer to Problem 7TY The probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is 0.0009. Explanation of Solution Given info: The standard deck consists of 52 playing cards. Calculation: In a standard deck of cards, there are 13 hearts, 13 diamonds, 13 spades and 13 clubs. Also, includes two jokers then the total number of cards is 54. The joker card can be used to represent any card. Thus, the total number of diamonds is 15. Combination Rule: There are n different items and r number of selections and the selections are made without replacement, then the number of different combinations (order does not matter counts) is given by, nCr = n! (n-r)!r! For choosing 5 cards: Here, the total number of kings (n) is 54 and the number of selected cards (r) is 5, the selections are made without replacement. Substitute 54 for *n* and 5 for 'r', then the number of different possible is 54! 54 Cs= (54-5)!5! 54! 4915! = 3.162, 510 =

Answer to Problem 7TY The probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is 0.0009. Explanation of Solution Given info: The standard deck consists of 52 playing cards. Calculation: In a standard deck of cards, there are 13 hearts, 13 diamonds, 13 spades and 13 clubs. Also, includes two jokers then the total number of cards is 54. The joker card can be used to represent any card. Thus, the total number of diamonds is 15. Combination Rule: There are n different items and r number of selections and the selections are made without replacement, then the number of different combinations (order does not matter counts) is given by, nCr = n! (n-r)!r! For choosing 5 cards: Here, the total number of kings (n) is 54 and the number of selected cards (r) is 5, the selections are made without replacement. Substitute 54 for *n* and 5 for 'r', then the number of different possible is 54! 54 Cs= (54-5)!5! 54! 4915! = 3.162, 510 =

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 9CYU
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Hi, Could you please explain to me how the answer comes out to 3,003 regarding choosing 5 diamonds. Thank you.

Answer to Problem 7TY The probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is 0.0009. Explanation of Solution Given info: The standard deck consists of 52 playing cards. Calculation: In a standard deck of cards, there are 13 hearts, 13 diamonds, 13 spades and 13 clubs. Also, includes two jokers then the total number of cards is 54. The joker card can be used to represent any card. Thus, the total number of diamonds is 15. Combination Rule: There are n different items and r number of selections and the selections are made without replacement, then the number of different combinations (order does not matter counts) is given by, nCr = n! (n-r)!r! For choosing 5 cards: Here, the total number of kings (n) is 54 and the number of selected cards (r) is 5, the selections are made without replacement. Substitute 54 for 'n' and 5 for 'r', then the number of different possible is 54! 54 Cs= (54-5)!5! 54! 4915! = 3, 162, 510 =
Transcribed Image Text:Answer to Problem 7TY The probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is 0.0009. Explanation of Solution Given info: The standard deck consists of 52 playing cards. Calculation: In a standard deck of cards, there are 13 hearts, 13 diamonds, 13 spades and 13 clubs. Also, includes two jokers then the total number of cards is 54. The joker card can be used to represent any card. Thus, the total number of diamonds is 15. Combination Rule: There are n different items and r number of selections and the selections are made without replacement, then the number of different combinations (order does not matter counts) is given by, nCr = n! (n-r)!r! For choosing 5 cards: Here, the total number of kings (n) is 54 and the number of selected cards (r) is 5, the selections are made without replacement. Substitute 54 for 'n' and 5 for 'r', then the number of different possible is 54! 54 Cs= (54-5)!5! 54! 4915! = 3, 162, 510 =
For choosing 5 diamonds: Here, the total number of diamonds (n) is 15 and the number of selected diamonds (r) is 5, the selections are made without replacement. Substitute 15 for 'n' and 5 for 'r', then the number of different possible is 15! 15 C5 = (15-5)!5! 15! 10!5! = 3,003 Then, the probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is, P (Five Diamonds includes two jokers) = 15C₁ 34 C5 3,003 3,162,510 = 0.0009 Thus, the probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is 0.0009. Interpretation: There is a 0.0009 probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers. < Previous Chapter 3.4, Problem 6TY Next > Chapter 3.4, Problem 8TY
Transcribed Image Text:For choosing 5 diamonds: Here, the total number of diamonds (n) is 15 and the number of selected diamonds (r) is 5, the selections are made without replacement. Substitute 15 for 'n' and 5 for 'r', then the number of different possible is 15! 15 C5 = (15-5)!5! 15! 10!5! = 3,003 Then, the probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is, P (Five Diamonds includes two jokers) = 15C₁ 34 C5 3,003 3,162,510 = 0.0009 Thus, the probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers is 0.0009. Interpretation: There is a 0.0009 probability being dealt 5 diamonds from a standard deck of playing cards that also includes two jokers. < Previous Chapter 3.4, Problem 6TY Next > Chapter 3.4, Problem 8TY
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