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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
From a Group of 8 People, Including George and Nina, 3 people are to b
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24 Sep 2022, 06:48
24 Sep 2022, 06:48
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Question Stats:
49% (02:34) correct
49% (01:59) wrong based on 14 sessions
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From a Group of 8 People, Including George and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include George but not Nina
A 5/56
B 9/56
C 15/56
D 21/56
E 25/56
A 5/56
B 9/56
C 15/56
D 21/56
E 25/56
Re: From a Group of 8 People, Including George and Nina, 3 people are to b
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28 Sep 2022, 07:00
28 Sep 2022, 07:00
Expert Reply
Number of ways of selecting 3 people out of 8 people = 8C3
In the three members George will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Lina = 6
Number of ways to form a 3 member team that includes George and excludes Lina = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
In the three members George will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Lina = 6
Number of ways to form a 3 member team that includes George and excludes Lina = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
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Joined: 12 Sep 2018
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Re: From a Group of 8 People, Including George and Nina, 3 people are to b
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07 Apr 2023, 06:55
07 Apr 2023, 06:55
1
Expert Reply
GeminiHeat wrote:
From a Group of 8 People, Including George and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include George but not Nina
A 5/56
B 9/56
C 15/56
D 21/56
E 25/56
A 5/56
B 9/56
C 15/56
D 21/56
E 25/56
We are given that 3 people are to be selected from 8 people and need to determine the probability that, of the 3 people selected, George is included but Nina is not. Let’s first determine the total number of ways to select 3 people from a group of 8.
The number of ways to select 3 people from a group of 8 is 8C3 = (8 x 7 x 6)/3! = 56.
Next, let’s determine the number of ways to select 3 people from a group of 8 when George is included but Nina is not.
Since George must be included and Nina is not, we can reduce the number of available spots from 3 to 2 (because George is already selected), and we can reduce the number of people available to be selected from 8 to 6 (Nina is not even considered, and George is already selected).
Thus, the number of ways to select 3 people when George is included and Nina is not is:
6C2 = (6 x 5)/2! = 15
So, finally, the probability of selecting a group of three with George and not Nina is:
15/56
Answer: C
