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COMEDK202510 May 2025Evening ShiftMathematicsProbabilityActual

Five persons entered the lift cabin on the ground floor of an eight-floor apartment. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first floor, then the probability of all five persons leaving at different floors is

Options

  1. A7 ^7 P₅
  2. B^7 P₅ 7^5
  3. C^7 P₅ 5^7
  4. D5! 7^5

Correct answer

B. ^7 P₅ 7^5

Step-by-step solution

There are 8 floors in the apartment, but the persons leave at any floor from the first to the eighth floor. Thus, there are 7 possible floors for each person to leave (1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th floor). Each of the 5 persons can choose any of the 7 floors independently. Therefore, the total number of ways for the 5 persons to leave the cabin is 7 7 7 7 7 = 7^5 . For all 5 persons to leave at different floors, we need to select 5 distinct floors out of the 7 available floors and assign them to the 5 pers

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