3. Determine whether the statement is true or false, If the statement is false, make the necessary change(s) to produce a true statement. When working problems involving probability with permutations, the denominators of the probability fractions consist of the total number of possible permutations,

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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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Question 3 

**Homework 11.5: Probability and Permutations**

1. **Fill in the blanks.**

   Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of ______ with comic E performing first divided by ______.

   Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of (1) ______ with comic E performing first divided by (2) ______.

   (1)
   - O permutations
   - O comics
   - O combinations

   (2)
   - O the total number of possible combinations.
   - O the number of comics.
   - O the total number of possible permutations.

2. **Fill in the blanks so that the resulting statement is true.**

   The probability of winning a lottery with one lottery ticket is the number of ways of winning, which is precisely ______, divided by the total number of possible ______.

   The probability of winning a lottery with one lottery ticket is the number of ways of winning, which is precisely 
   
   ______, divided by the total number of possible (2) ______.

   (1)
   - O the number of combinations,
   - O permutations.
   - O combinations.

   (2)
   - O the number of permutations,
   
3. **Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.**

   When working problems involving probability with permutations, the denominators of the probability fractions consist of the total number of possible permutations.

   Choose the correct answer below.

   - O A. The statement is true.
   - O B. The statement is false. When working problems involving probability with permutations, the numerators of the probability fractions consist of the total number of possible permutations.
   - O C. The statement is false. When working problems involving probability with combinations, the denominators of the probability fractions consist of the total number of possible permutations.
   - O D. The statement is false. When working problems involving probability with combinations, the numerators of the probability fractions consist of the total number of possible
Transcribed Image Text:**Homework 11.5: Probability and Permutations** 1. **Fill in the blanks.** Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of ______ with comic E performing first divided by ______. Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of (1) ______ with comic E performing first divided by (2) ______. (1) - O permutations - O comics - O combinations (2) - O the total number of possible combinations. - O the number of comics. - O the total number of possible permutations. 2. **Fill in the blanks so that the resulting statement is true.** The probability of winning a lottery with one lottery ticket is the number of ways of winning, which is precisely ______, divided by the total number of possible ______. The probability of winning a lottery with one lottery ticket is the number of ways of winning, which is precisely ______, divided by the total number of possible (2) ______. (1) - O the number of combinations, - O permutations. - O combinations. (2) - O the number of permutations, 3. **Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.** When working problems involving probability with permutations, the denominators of the probability fractions consist of the total number of possible permutations. Choose the correct answer below. - O A. The statement is true. - O B. The statement is false. When working problems involving probability with permutations, the numerators of the probability fractions consist of the total number of possible permutations. - O C. The statement is false. When working problems involving probability with combinations, the denominators of the probability fractions consist of the total number of possible permutations. - O D. The statement is false. When working problems involving probability with combinations, the numerators of the probability fractions consist of the total number of possible
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