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There are five students S1, S2, S3, S4 and S5 in a class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.
The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is
The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is
- a)3/40
- b)1/8
- c)7/40
- d)1/5
Correct answer is option 'A'. Can you explain this answer?
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There are five students S1, S2, S3, S4and S5in a class and for them th...
This is the case of de arrangement
n(A) = No. of ways of deranging 4 objects
n(A) = No. of ways of deranging 4 objects
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There are five students S1, S2, S3, S4and S5in a class and for them th...
Key Points:
- There are 5 students and 5 seats arranged in a row.
- Initially, each student is assigned a specific seat.
- On the examination day, the seats are randomly allotted to the students.
- We need to find the probability that S1 gets R1 and none of the remaining students get their previously allotted seats.
Solution:
To solve this problem, we can consider all possible scenarios and count the favorable outcomes.
Scenario 1: S1 gets R1
In this scenario, we have fixed the seat for S1. Now, we need to assign the remaining seats to the other students.
Sub-scenario 1: S2 gets R2
In this sub-scenario, we have fixed the seats for both S1 and S2. Now, we need to assign the remaining seats to the remaining students.
Sub-sub-scenario 1: S3 gets R3
In this sub-sub-scenario, we have fixed the seats for S1, S2, and S3. Now, we need to assign the remaining seats to the remaining students.
Sub-sub-sub-scenario 1: S4 gets R4
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, all students have been assigned seats different from their initially allotted seats. Therefore, this is a favorable outcome.
Sub-sub-sub-scenario 2: S4 gets R5
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, S5 gets his initially allotted seat R5. Therefore, this is not a favorable outcome.
Therefore, in the sub-sub-scenario 1, we have one favorable outcome and one unfavorable outcome. Hence, the probability of this sub-sub-scenario is 1/2.
Sub-sub-scenario 2: S3 gets R4
In this sub-sub-scenario, we have fixed the seats for S1, S2, and S3. Now, we need to assign the remaining seats to the remaining students.
Sub-sub-sub-scenario 1: S4 gets R5
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, S5 gets his initially allotted seat R5. Therefore, this is not a favorable outcome.
Sub-sub-sub-scenario 2: S4 gets R1
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, S5 gets his initially allotted seat R1. Therefore, this is not a favorable outcome.
Therefore, in the sub-sub-scenario 2, we have zero favorable outcomes. Hence, the probability of this sub-sub-scenario
- There are 5 students and 5 seats arranged in a row.
- Initially, each student is assigned a specific seat.
- On the examination day, the seats are randomly allotted to the students.
- We need to find the probability that S1 gets R1 and none of the remaining students get their previously allotted seats.
Solution:
To solve this problem, we can consider all possible scenarios and count the favorable outcomes.
Scenario 1: S1 gets R1
In this scenario, we have fixed the seat for S1. Now, we need to assign the remaining seats to the other students.
Sub-scenario 1: S2 gets R2
In this sub-scenario, we have fixed the seats for both S1 and S2. Now, we need to assign the remaining seats to the remaining students.
Sub-sub-scenario 1: S3 gets R3
In this sub-sub-scenario, we have fixed the seats for S1, S2, and S3. Now, we need to assign the remaining seats to the remaining students.
Sub-sub-sub-scenario 1: S4 gets R4
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, all students have been assigned seats different from their initially allotted seats. Therefore, this is a favorable outcome.
Sub-sub-sub-scenario 2: S4 gets R5
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, S5 gets his initially allotted seat R5. Therefore, this is not a favorable outcome.
Therefore, in the sub-sub-scenario 1, we have one favorable outcome and one unfavorable outcome. Hence, the probability of this sub-sub-scenario is 1/2.
Sub-sub-scenario 2: S3 gets R4
In this sub-sub-scenario, we have fixed the seats for S1, S2, and S3. Now, we need to assign the remaining seats to the remaining students.
Sub-sub-sub-scenario 1: S4 gets R5
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, S5 gets his initially allotted seat R5. Therefore, this is not a favorable outcome.
Sub-sub-sub-scenario 2: S4 gets R1
In this sub-sub-sub-scenario, we have fixed the seats for S1, S2, S3, and S4. Now, we need to assign the remaining seat to S5.
In this sub-sub-sub-scenario, S5 gets his initially allotted seat R1. Therefore, this is not a favorable outcome.
Therefore, in the sub-sub-scenario 2, we have zero favorable outcomes. Hence, the probability of this sub-sub-scenario
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There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer?
Question Description
There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer?.
There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer?.
Solutions for There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer?, a detailed solution for There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice There are five students S1, S2, S3, S4and S5in a class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her isa)3/40b)1/8c)7/40d)1/5Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
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