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RohitSaluja
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03 Aug 2020, 00:58
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Q1. Alex and Erin are two of the eight students trying out for a certain five-person chess team. If Alex and Erin must make it to the chess team, in how many different ways can the chess team be populated?
Q2. In a treasure chest, there are five different flawed diamonds and three different perfect diamonds. If a pirate selects four diamonds from the chest, in how many ways can four diamonds be selected, if exactly two of them must be perfect diamonds?
While solving Q1, we assumed that both Alex and Erin are already part of the chess team which leaves us to select three players to choose from six, hence 6 chooses 3. but In Q2 if I assume the same as in Q1 that two perfect diamonds have already been chosen then I would just need to select 2 flawed diamonds from a set of 5 which is 5 chooses 2 but that's not the answer. What am I missing on Q2?
Q2. In a treasure chest, there are five different flawed diamonds and three different perfect diamonds. If a pirate selects four diamonds from the chest, in how many ways can four diamonds be selected, if exactly two of them must be perfect diamonds?
While solving Q1, we assumed that both Alex and Erin are already part of the chess team which leaves us to select three players to choose from six, hence 6 chooses 3. but In Q2 if I assume the same as in Q1 that two perfect diamonds have already been chosen then I would just need to select 2 flawed diamonds from a set of 5 which is 5 chooses 2 but that's not the answer. What am I missing on Q2?
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globaldesi
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RohitSaluja
In question 2 how do you know which are the two flawed diamonds.
All you are saying is from rest 5 select 2 diamonds.
Q1 and Q2 are not same
If i were to solve Q2 , I would rather say
select 2 from 3 perfect diamonds and select both flawed diamonds.
that is 3 c2 and 2c2 = 3
05 Aug 2020, 09:16
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RohitSaluja
Hi RohitSaluja
Q1. Alex and Erin are two of the eight students trying out for a certain five-person chess team. If Alex and Erin must make it to the chess team, in how many different ways can the chess team be populated?
(8-2)C(5-2) = 6C3
Q2. In a treasure chest, there are five different flawed diamonds and three different perfect diamonds. If a pirate selects four diamonds from the chest, in how many ways can four diamonds be selected, if exactly two of them must be perfect diamonds?
5C2*3C2
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Hi there,
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