A firm works 5 days a week. Every employee works 3 full days and 2 half days. A half day can be either morning or afternoon and cannot be on the same day.

Monday, 22 April 2019

7:55 PM

 

 

A firm works 5 days a week. Every empoloyee works 3 full days and 2 half days. A half day can be either morning or afternoon and cannot be on the same day. a) If the firm has 115 employees, how many people must have the same work schedule? Submit part Your answer is numerically correct. You were awarded 1 mark. You scored 1 mark for this part. Score: 1/1 Answered b) What is the smallest number of employees that guarantees at least 5 workers have exactly the same schedule? 161 Submit part Your answer is numerically correct. You were awarded 1 mark. You scored 1 mark for this part. Score: 1/1

 

A firm works 5 days a week. Every empoloyee works 3 full days and 2 half days. A half day can be either morning or afternoon and cannot be on the same day. a) If the firm has 129 employees, how many people must have the same work schedule? 4 Expected answer:

 

The number of possible schedules is

Apply pigeonhole

 

Machine generated alternative text: a) By the pigeonhole principle, there are at least 129 40 people with the same schedule. = [3.2251 — 4

 

 

 

b) What is the smallest number of employees that guarantees at least 3 workers have exactly the same schedule? 81 81 81 81 Expected answer:

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c) What is the largest number of employees that does not guarantee there are at least 4 employess with exactly the same schedule? 120 120 120 Expected answer: 120

 

 

 

 

 

 

b and c) In order to achieve at least 3 people with the same schedule by the pigeonhole principle, we need where is the number of workers. Hence 80 < T 120. Which produces the answers for parts b and c.

 

 

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