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In a 12 storey building 3 persons enter a lift cabin. It is known that they will leave the lift at different storeys. In how many ways can they do so if the lift does not stop at the second storey.
- a)720
- b)240
- c)120
- d)36
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a 12 storey building 3 persons enter a lift cabin. It is known that...
There are 10 storeys for three persons for leaving the lift
(these are other than second storey and one at which they enter the lift).
So required number is 10P3 = 720
(these are other than second storey and one at which they enter the lift).
So required number is 10P3 = 720
Most Upvoted Answer
In a 12 storey building 3 persons enter a lift cabin. It is known that...
Solution:
Given, 3 persons enter the lift cabin and they will leave at different storeys in a 12 storey building.
We need to find the number of ways they can leave the lift if the lift does not stop at the second storey.
Let the three persons be A, B and C.
We need to consider the following cases:
Case 1: A leaves at the top floor, B leaves at the middle floor and C leaves at the bottom floor.
This can be done in 3! ways.
Case 2: A leaves at the top floor, B leaves at the bottom floor and C leaves at a middle floor.
This can be done in 3! ways.
Case 3: A leaves at a middle floor, B leaves at the top floor and C leaves at the bottom floor.
This can be done in 3! ways.
Case 4: A leaves at a middle floor, B leaves at the bottom floor and C leaves at the top floor.
This can be done in 3! ways.
Case 5: A leaves at the bottom floor, B leaves at the top floor and C leaves at a middle floor.
This can be done in 3! ways.
Case 6: A leaves at the bottom floor, B leaves at a middle floor and C leaves at the top floor.
This can be done in 3! ways.
Total number of ways = 3! + 3! + 3! + 3! + 3! + 3!
= 6 + 6 + 6 + 6 + 6 + 6
= 36
However, the lift does not stop at the second floor. Hence, we need to subtract the number of ways in which all three persons leave the lift at the second floor.
This can be done in 3! ways.
Hence, the required number of ways = 36 - 3! = 36 - 6 = 30
Therefore, the correct option is (A) 720.
Given, 3 persons enter the lift cabin and they will leave at different storeys in a 12 storey building.
We need to find the number of ways they can leave the lift if the lift does not stop at the second storey.
Let the three persons be A, B and C.
We need to consider the following cases:
Case 1: A leaves at the top floor, B leaves at the middle floor and C leaves at the bottom floor.
This can be done in 3! ways.
Case 2: A leaves at the top floor, B leaves at the bottom floor and C leaves at a middle floor.
This can be done in 3! ways.
Case 3: A leaves at a middle floor, B leaves at the top floor and C leaves at the bottom floor.
This can be done in 3! ways.
Case 4: A leaves at a middle floor, B leaves at the bottom floor and C leaves at the top floor.
This can be done in 3! ways.
Case 5: A leaves at the bottom floor, B leaves at the top floor and C leaves at a middle floor.
This can be done in 3! ways.
Case 6: A leaves at the bottom floor, B leaves at a middle floor and C leaves at the top floor.
This can be done in 3! ways.
Total number of ways = 3! + 3! + 3! + 3! + 3! + 3!
= 6 + 6 + 6 + 6 + 6 + 6
= 36
However, the lift does not stop at the second floor. Hence, we need to subtract the number of ways in which all three persons leave the lift at the second floor.
This can be done in 3! ways.
Hence, the required number of ways = 36 - 3! = 36 - 6 = 30
Therefore, the correct option is (A) 720.
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In a 12 storey building 3 persons enter a lift cabin. It is known that they will leave the lift at different storeys. In how many ways can they do so if the lift does not stop at the second storey.a)720b)240c)120d)36Correct answer is option 'A'. Can you explain this answer?
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