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Difficulty:
75%
(hard)
Question Stats:
48% (01:56) correct
52%
(01:35)
wrong
based on 388
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Every night, Jon and his brothers randomly determine the schedule in which they will get to use the shower in the morning. How many distinct schedules are possible?
(1) The probability that Jon will be first or last is 40%.
(2) There are 48 ways Jon could be first or last.
(1) The probability that Jon will be first or last is 40%.
(2) There are 48 ways Jon could be first or last.
03 Jul 2014, 12:20
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Every night, Jon and his brothers randomly determine the schedule in which they will get to use the shower in the morning. How many distinct schedules are possible?
Say there are n brothers including Jon. The number of distinct schedules would be n!.
(1) The probability that Jon will be first or last is 40%. The probability that Jon will be first is 1/n and the probability that he'll be last will also be 1/n. Thus we have that 1/n + 1/n = 0.4 --> n = 5. Sufficient.
(2) There are 48 ways Jon could be first or last. {Jon}{# of arrangements of other brothers} + {# of arrangements of other brothers}{Jon} = 48 --> (n-1)! + (n-1)! = 48 --> (n-1)! = 24 --> n = 5. Sufficient.
Answer: D.
Hope it's clear.
Say there are n brothers including Jon. The number of distinct schedules would be n!.
(1) The probability that Jon will be first or last is 40%. The probability that Jon will be first is 1/n and the probability that he'll be last will also be 1/n. Thus we have that 1/n + 1/n = 0.4 --> n = 5. Sufficient.
(2) There are 48 ways Jon could be first or last. {Jon}{# of arrangements of other brothers} + {# of arrangements of other brothers}{Jon} = 48 --> (n-1)! + (n-1)! = 48 --> (n-1)! = 24 --> n = 5. Sufficient.
Answer: D.
Hope it's clear.
General Discussion
Siddharth108
Joined: 27 Sep 2020
Last visit: 16 Mar 2023
Posts: 6
Own Kudos:
Given Kudos: 113
Location: India
Schools: Rotman '25 (S) Schulich Sep'23 intake (A)
GMAT 1: 690 Q48 V36
GMAT 2: 700 Q48 V38
06 Apr 2021, 04:47
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Bunuel
Hi Bunuel,
Could you please explain Statement (2)? How did (n-1)! + (n-1)! equal to 48, i.e. the number of ways Jon could be first OR last?
Thank you.
