Question 5. Determine whether the following statements are true or false.Justify your answers.(i) At any party, the number of people who have shaken the hand of an oddnumber of people is even.(ii) It is possible to have a party of 11 people, each of whom know exactly 5of the others.

Answered: Question 5. Determine whether the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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The median yearly salary paid to the 24 players on a soccer team is $24,000 less than the median yearly salary paid to the 12 players on a basketball team. Based on this information, which of the following statements must be true? a The highest-paid soccer player earns more than the lowest-paid basketball player. All 12 players on the basketball team earn more than each player on the soccer team. At least one of the basketball players ears exactly $24,000 more than one of the soccer players. The 6 highest-paid basketball players each earn more than each of the 12 lowest-paid soccer players.
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A classroom contains 30 distinct children and 50 books. Every child collects one book (and books may not be shared). Write down expressions for the number of different possible outcomes in each of the following cases: i. All books are distinct. ii. All books are identical. iii. 49 books are identical and 1 is different. iv. 48 books are distinct and different from the 2 final books which are identical. Which of your answers above is the largest?
. Suppose you are working on a ten-digit keypad to open a door. You know the combination is exactly three digits long.1. How many choices are there if you may use a number multiple times and the order matters?2. How many choices are there if you may not use a number multiple times and the order matters?3. How many choices are there if you may not use a number multiple times and the order doesnot matter?4. How many choices are there if you may use a number multiple times and the order does notmatter?
There are 40 men in class. 29 of them have no facial hair (i.e. neither a beard nor a mustache). If 7 of the men have beards and 9 of the men have mustaches, how many of the men in the class have both a beard and a mustache? O A. 2 В. 4 O c. 5 D. 7 ОЕ. 16

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Question 5. Determine whether the following statements are true or false. Justify your answers. (i) At any party, the number of people who have shaken the hand of an odd number of people is even. (ii) It is possible to have a party of 11 people, each of whom know exactly 5 of the others.