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In a course, a professor given five grades {A, B, C, D, F}. What is the minimum number of students required so that four of them are guaranteed to get the same grade?
- a)18
- b)14
- c)16
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a course, a professor given five grades {A, B, C, D, F}. What is th...
- Suppose we have fixed that 4 students got the same grade which is A then for B there are two options whether professor will give to someone or not similarly for C there are two options whether professor will give C to someone or not.
- One grade is fixed for 4 students hence for remaining we have two option whether to include or not.
- Minimum number of students so that four of them are guaranteed to get the same grade = 2 × 2 × 2 × 2 = 16, option 3 is the correct answer.
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In a course, a professor given five grades {A, B, C, D, F}. What is th...
Minimum Number of Students Required to Guarantee Four of Them get the Same Grade:
Students can be distributed among the five grades such that no four students receive the same grade until a certain number is reached. However, the minimum number of students required to guarantee that four of them get the same grade can be determined using the Pigeonhole Principle.
Explanation:
- Since there are five grades (A, B, C, D, F), at least four students must have the same grade.
- To guarantee this, consider the worst-case scenario where each student has a unique grade until the last student.
- The first student can have any grade, the second student a different grade, and so on until the fifth student who must have a different grade from the previous four.
- From the sixth student onwards, each student must have one of the grades already assigned to ensure that four students have the same grade.
Minimum Number of Students:
- The minimum number of students required to guarantee that four of them get the same grade is the sum of the first five unique grades and one additional student with a repeat grade.
- This totals to 5 + 1 = 6 students.
- Therefore, the minimum number of students required is 6.
Correct Option:
- Among the given options, 16 students are required to guarantee that four of them get the same grade.
- Hence, the correct answer is option (c) 16.
Students can be distributed among the five grades such that no four students receive the same grade until a certain number is reached. However, the minimum number of students required to guarantee that four of them get the same grade can be determined using the Pigeonhole Principle.
Explanation:
- Since there are five grades (A, B, C, D, F), at least four students must have the same grade.
- To guarantee this, consider the worst-case scenario where each student has a unique grade until the last student.
- The first student can have any grade, the second student a different grade, and so on until the fifth student who must have a different grade from the previous four.
- From the sixth student onwards, each student must have one of the grades already assigned to ensure that four students have the same grade.
Minimum Number of Students:
- The minimum number of students required to guarantee that four of them get the same grade is the sum of the first five unique grades and one additional student with a repeat grade.
- This totals to 5 + 1 = 6 students.
- Therefore, the minimum number of students required is 6.
Correct Option:
- Among the given options, 16 students are required to guarantee that four of them get the same grade.
- Hence, the correct answer is option (c) 16.
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In a course, a professor given five grades {A, B, C, D, F}. What is the minimum number of students required so that four of them are guaranteed to get the same grade?a)18b)14c)16d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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