Five persons enter a lift on the ground floor of an eight-floor apartment. Assuming that each of them independentlyand with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the five persons are leaving the lift at different floors?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?

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Five persons enter a lift on the ground floor of an eight-floor apartment. Assuming that each of them independently and with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the five persons are leaving the lift at different floors?

Correct answer is option 'C'. Can you explain this answer?

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Five persons enter a lift on the ground floor of an eight-floor apartm...

Apart from the ground floor, there are 7 floors
Let's find out the total number of ways in which all the five persons can leave the lift at seven different floors
The 1st person can leave the lift in any of the 7 floors (7 ways)
The 2nd person can leave the lift in any of the remaining 6 floors (6 ways)
The 3nd person can leave the lift in any of the remaining 5 floors (5 ways) ...
The 5th person can leave the lift in any of the remaining 3 floors (3 ways)
Total number of ways

n(E)= Total Number of ways in which all the five persons can leave the lift at seven different floors

Now we will find out the total number of ways in which each of the five persons can leave the lift at any of the seven floors
The 1st person can leave the lift in any of the 7 floors (7 ways)
The 2nd person can leave the lift in any of the 7 floors (7 ways)
The 3nd person can leave the lift in any of the 7 floors (7 ways)
...
The 5th person can leave the lift in any of the 7 floors (7 ways)
Total number of ways = 7 × 7 × 7 × 7 × 7 = 7⁵
i.e., The total number of ways in which each the five persons can leave the lift at any of the seven floors = n(S) = 7⁵.
Then, the probability that all the five persons are leaving the lift at different floors

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Five persons enter a lift on the ground floor of an eight-floor apartment. Assuming that each of them independentlyand with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the five persons are leaving the lift at different floors?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?

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Five persons enter a lift on the ground floor of an eight-floor apartment. Assuming that each of them independentlyand with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the five persons are leaving the lift at different floors?a)b)c)d)Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Five persons enter a lift on the ground floor of an eight-floor apartment. Assuming that each of them independentlyand with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the five persons are leaving the lift at different floors?a)b)c)d)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five persons enter a lift on the ground floor of an eight-floor apartment. Assuming that each of them independentlyand with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the five persons are leaving the lift at different floors?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?.

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