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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
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
From a Group of 8 People, Including George and Nina, 3 people are to b...
In a group of 8 people that includes George and Nina, we need to select 3 people randomly for a project. The objective is to choose a group that includes George but excludes Nina.
To meet this requirement, we consider that George must be included in the selection. Therefore, we only need to choose 2 additional people from the remaining 6 individuals (excluding Nina).
The number of ways to choose 2 people from a group of 6 can be calculated as 6C2, which is equal to 15.
The total number of ways to select 3 people from a group of 8 can be calculated as 8C3, which equals 56.
Hence, the probability of selecting the desired group, which includes George but excludes Nina, is 15/56.
Therefore, the answer is C: 15/56.
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Community Answer
From a Group of 8 People, Including George and Nina, 3 people are to b...
Understanding the Problem
To find the probability of selecting 3 people including George but not Nina from a group of 8, we need to break down the selection process.
Total Group Composition
- The total number of people: 8 (including George and Nina)
- We need to select 3 people such that:
- George is included
- Nina is excluded
Selection Process
1. Choose George: Since George must be included, we automatically select him.
2. Exclude Nina: We now have 6 remaining candidates (8 total - 2 (George and Nina)).
3. Select 2 more people from the remaining 6: We need to choose 2 additional members from the remaining 6 people.
The number of ways to choose 2 people from 6 can be calculated using the combination formula:
\[
\text{C}(n, k) = \frac{n!}{k!(n-k)!}
\]
where \( n \) is the total number of items to choose from, and \( k \) is the number of items to choose.
So, we compute:
\[
\text{C}(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15
\]
Total Possible Selections
- The total ways to select any 3 people from the original group of 8 is:
\[
\text{C}(8, 3) = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56
\]
Calculating the Probability
- The probability of selecting 3 people that include George but not Nina is:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{15}{56}
\]
Conclusion
Thus, the correct answer is option C: 15/56.
To find the probability of selecting 3 people including George but not Nina from a group of 8, we need to break down the selection process.
Total Group Composition
- The total number of people: 8 (including George and Nina)
- We need to select 3 people such that:
- George is included
- Nina is excluded
Selection Process
1. Choose George: Since George must be included, we automatically select him.
2. Exclude Nina: We now have 6 remaining candidates (8 total - 2 (George and Nina)).
3. Select 2 more people from the remaining 6: We need to choose 2 additional members from the remaining 6 people.
The number of ways to choose 2 people from 6 can be calculated using the combination formula:
\[
\text{C}(n, k) = \frac{n!}{k!(n-k)!}
\]
where \( n \) is the total number of items to choose from, and \( k \) is the number of items to choose.
So, we compute:
\[
\text{C}(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15
\]
Total Possible Selections
- The total ways to select any 3 people from the original group of 8 is:
\[
\text{C}(8, 3) = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56
\]
Calculating the Probability
- The probability of selecting 3 people that include George but not Nina is:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{15}{56}
\]
Conclusion
Thus, the correct answer is option C: 15/56.
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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)5/56b)9/56c)15/56d)21/56e)25/56Correct answer is option 'C'. Can you explain this answer?
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