In a state pick 4 lottery game, a bettor selects four numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same order. Do the calculations for this lottery involve the combinations rule or either of the two permutations rules? Why or why not? If not, what rule does apply? Choose the correct answer below. O A. The permutation rule (with some identical items) applies to this problem because repetition is allowed. The permutation rule (with different items) and the combination rule cannot be used with repetition. O B. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The multiplication counting rule applies to this problem. OC. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The factorial rule applies to this problem O D. The permutation rule (with different items) applies to this problem because repetition is allowed. The permutation rule (with some identical items) and the combination rule cannot be used with repetition. O E. The combination rule applies to this problem because the numbers are selected with replacement. Neither of the permutations rules allows replacement.
In a state pick 4 lottery game, a bettor selects four numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same order. Do the calculations for this lottery involve the combinations rule or either of the two permutations rules? Why or why not? If not, what rule does apply? Choose the correct answer below. O A. The permutation rule (with some identical items) applies to this problem because repetition is allowed. The permutation rule (with different items) and the combination rule cannot be used with repetition. O B. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The multiplication counting rule applies to this problem. OC. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The factorial rule applies to this problem O D. The permutation rule (with different items) applies to this problem because repetition is allowed. The permutation rule (with some identical items) and the combination rule cannot be used with repetition. O E. The combination rule applies to this problem because the numbers are selected with replacement. Neither of the permutations rules allows replacement.
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...
Related questions
Concept explainers
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.
Topic Video
Question
Transcribed Image Text:In a state pick 4 lottery game, a bettor selects four numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same
order. Do the calculations for this lottery involve the combinations rule or either of the two permutations rules? Why or why not? If not, what rule does apply?
Choose the correct answer below.
O A. The permutation rule (with some identical items) applies to this problem because repetition is allowed. The permutation rule (with different items) and the combination rule cannot be used with repetition.
O B. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The multiplication counting rule applies to this problem.
OC. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The factorial rule applies to this problem.
O D. The permutation rule (with different items) applies to this problem because repetition is allowed. The permutation rule (with some identical items) and the combination rule cannot be used with repetition.
O E. The combination rule applies to this problem because the numbers are selected with replacement. Neither of the permutations rules allows replacement.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning