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Four persons enter a lift on the ground floor of an 8-floor building

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Four persons enter a lift on the ground floor of an 8-floor building  [#permalink]

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New post 08 Mar 2019, 05:17
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A
B
C
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E

Difficulty:

  45% (medium)

Question Stats:

63% (02:33) correct 38% (02:59) wrong based on 16 sessions

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Four persons enter a lift on the ground floor of an 8-floor building(excluding the ground floor). Each person is equally likely to leave the lift on any floor except the ground floor. What is the probability of all the persons leaving the lift on different floors?

A. 105/512

B. 105/256

C. 112/243

D. 1560/2147

E. 7/8

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Re: Four persons enter a lift on the ground floor of an 8-floor building  [#permalink]

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New post 08 Mar 2019, 08:05
gmat1393 wrote:
Four persons enter a lift on the ground floor of an 8-floor building(excluding the ground floor). Each person is equally likely to leave the lift on any floor except the ground floor. What is the probability of all the persons leaving the lift on different floors?

A. 105/512

B. 105/256

C. 112/243

D. 1560/2147

E. 7/8


Out of 4 persons (Let, A, B, C and D) the first person has 8 choices (each at a floor) to leave the lift

The second person also has 8 choices to leave the lift

Likewise total possibilities of people to leave lift at floors = 8*8*8*8

Favourable ways to leave the lift
First person has 8 choices, second has 7 choices, third has 6 choices and forth has 5 choices so total ways = 8*7*6*5

Favourable Probability = (8*7*6*5) / (8*8*8*8) = 105 / 256

Answer: Option B
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Re: Four persons enter a lift on the ground floor of an 8-floor building  [#permalink]

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New post 08 Mar 2019, 09:50
gmat1393 wrote:
Four persons enter a lift on the ground floor of an 8-floor building(excluding the ground floor). Each person is equally likely to leave the lift on any floor except the ground floor. What is the probability of all the persons leaving the lift on different floors?

A. 105/512

B. 105/256

C. 112/243

D. 1560/2147

E. 7/8


total floors where 4 persons can get down ; 8^4
and since each person is likely to get down on different floor ; 8*7*6*5
8*7*6*5 /8^4 = 105/256
IMO B
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Re: Four persons enter a lift on the ground floor of an 8-floor building   [#permalink] 08 Mar 2019, 09:50
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Four persons enter a lift on the ground floor of an 8-floor building

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