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KARISHMA315
Joined: 09 May 2016
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Concentration: Finance, General Management
Schools: Wharton EMBA'26 (A) Yale (A)
GMAT 1: 710 Q49 V38
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23 Feb 2020, 10:15
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I read this below explanation in target test prep but I am not sure of this logic .
In a question where 3 people are to be selected in a pool of 5 people to form a writing club, two of the people can never be chosen together, in how many different ways can the club be composed?
They gave a formula in the explanation :
Total no of 3 club configuration that can be made = Total no of 3 club configuration in which both people are together in the club + Total no of 3 Person club configuration in which both people are not together in the club
They mentioned the 2 states are mutually exclusive and collectively exhaustive . But what about the scenario when 1 person is in the club and other is not . That is not part of the above formula and hence it is not collectively exhaustive.
Can someone pls clarify what I am missing here .
Thank you
In a question where 3 people are to be selected in a pool of 5 people to form a writing club, two of the people can never be chosen together, in how many different ways can the club be composed?
They gave a formula in the explanation :
Total no of 3 club configuration that can be made = Total no of 3 club configuration in which both people are together in the club + Total no of 3 Person club configuration in which both people are not together in the club
They mentioned the 2 states are mutually exclusive and collectively exhaustive . But what about the scenario when 1 person is in the club and other is not . That is not part of the above formula and hence it is not collectively exhaustive.
Can someone pls clarify what I am missing here .
Thank you
26 Feb 2020, 09:30
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“Total no of 3 Person club configuration in which both people are not together in the club”
Read carefully again...”both ppl are not together in the club”
Maybe one of them is in, or neither of them is in .....
Posted from my mobile device
Read carefully again...”both ppl are not together in the club”
Maybe one of them is in, or neither of them is in .....
Posted from my mobile device
26 Feb 2020, 20:43
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The scenario when one of the writers is selected and the other one is not selected is included in "total no of 3 Person club configuration in which both people are not together in the club". That part of the formula includes every possible scenario besides the scenario where the two writers are both together in the club; namely it includes the scenario where the first writer is in the club but the second is not, the second writer is in the club but the first writer is not and the scenario where neither of the writers are in the club. Notice that the sentence "total no of 3 Person club configuration in which both people are not together in the club" differs from the sentence "total no of 3 person club configuration in which neither of the two people are in the club".
As an alternative solution, one can calculate the number of ways for each of the three scenarios mentioned above and add.
As an alternative solution, one can calculate the number of ways for each of the three scenarios mentioned above and add.
