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Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?
- a)20
- b)30
- c)10
- d)60
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Five seats are vacant in a railway compartment, then in how many ways ...
Problem:
Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?
Solution:
To solve this problem, we can use the concept of permutations and combinations.
Step 1: Understand the problem
We have 5 vacant seats in a railway compartment and 3 passengers who need to be seated on these seats. We need to find the number of ways in which these 3 passengers can be seated.
Step 2: Analyze the problem
Since the order of seating is important, we need to use permutations to find the number of ways in which the passengers can be seated.
Step 3: Apply permutations
To find the number of ways to seat 3 passengers out of 5 vacant seats, we can use the formula for permutations:
nPr = n! / (n-r)!
Where n is the total number of items and r is the number of items to be selected.
In this case, n = 5 (number of vacant seats) and r = 3 (number of passengers).
So, the number of ways to seat 3 passengers on 5 vacant seats is:
5P3 = 5! / (5-3)! = 5! / 2! = 5 * 4 * 3 * 2 * 1 / (2 * 1) = 60
Therefore, there are 60 ways in which the 3 passengers can be seated on the 5 vacant seats.
Step 4: Final answer
The correct answer is option D, 60.
Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?
Solution:
To solve this problem, we can use the concept of permutations and combinations.
Step 1: Understand the problem
We have 5 vacant seats in a railway compartment and 3 passengers who need to be seated on these seats. We need to find the number of ways in which these 3 passengers can be seated.
Step 2: Analyze the problem
Since the order of seating is important, we need to use permutations to find the number of ways in which the passengers can be seated.
Step 3: Apply permutations
To find the number of ways to seat 3 passengers out of 5 vacant seats, we can use the formula for permutations:
nPr = n! / (n-r)!
Where n is the total number of items and r is the number of items to be selected.
In this case, n = 5 (number of vacant seats) and r = 3 (number of passengers).
So, the number of ways to seat 3 passengers on 5 vacant seats is:
5P3 = 5! / (5-3)! = 5! / 2! = 5 * 4 * 3 * 2 * 1 / (2 * 1) = 60
Therefore, there are 60 ways in which the 3 passengers can be seated on the 5 vacant seats.
Step 4: Final answer
The correct answer is option D, 60.
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Question Description
Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?a)20b)30c)10d)60Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?a)20b)30c)10d)60Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?a)20b)30c)10d)60Correct answer is option 'D'. Can you explain this answer?.
Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?a)20b)30c)10d)60Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?a)20b)30c)10d)60Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?a)20b)30c)10d)60Correct answer is option 'D'. Can you explain this answer?.
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