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A team of 3 students is to be selected out of 4 study groups, each study group containing 4 students. What is the number of different teams that can be selected if more than one student cannot be selected from a study group?
- a)24
- b)256
- c)536
- d)544
- e)1536
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A team of 3 students is to be selected out of 4 study groups, each stu...
Step 1: From 4 groups, select 3 groups.
This can be done in 4C3 ways
Step 2: From each of the three groups select one student
This can be done in 4C1 * 4C1 * 4C1 ways
Total = 44 = 256
Option is B.
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Community Answer
A team of 3 students is to be selected out of 4 study groups, each stu...
Understanding the Problem
To select a team of 3 students from 4 study groups, where each group has 4 students and no more than one student can be selected from any group, we need to follow a systematic approach.
Step 1: Choose Study Groups
- We need to choose 3 different study groups out of the 4 available groups.
- The number of ways to choose 3 study groups from 4 is calculated using the combination formula \( C(n, k) \), where \( n \) is the total number of groups and \( k \) is the number of groups to choose.
\[
C(4, 3) = \frac{4!}{3!(4-3)!} = 4
\]
Step 2: Select Students
- From each of the 3 selected study groups, we can choose 1 student. Since each group contains 4 students, the number of ways to select 1 student from each group is \( 4^3 \) because for each of the 3 groups, we have 4 options.
\[
4^3 = 64
\]
Step 3: Calculate Total Teams
- Multiply the number of ways to choose the study groups by the number of ways to select the students.
\[
\text{Total Teams} = C(4, 3) \times 4^3 = 4 \times 64 = 256
\]
Conclusion
Thus, the total number of different teams that can be selected is 256.
This matches option B.
To select a team of 3 students from 4 study groups, where each group has 4 students and no more than one student can be selected from any group, we need to follow a systematic approach.
Step 1: Choose Study Groups
- We need to choose 3 different study groups out of the 4 available groups.
- The number of ways to choose 3 study groups from 4 is calculated using the combination formula \( C(n, k) \), where \( n \) is the total number of groups and \( k \) is the number of groups to choose.
\[
C(4, 3) = \frac{4!}{3!(4-3)!} = 4
\]
Step 2: Select Students
- From each of the 3 selected study groups, we can choose 1 student. Since each group contains 4 students, the number of ways to select 1 student from each group is \( 4^3 \) because for each of the 3 groups, we have 4 options.
\[
4^3 = 64
\]
Step 3: Calculate Total Teams
- Multiply the number of ways to choose the study groups by the number of ways to select the students.
\[
\text{Total Teams} = C(4, 3) \times 4^3 = 4 \times 64 = 256
\]
Conclusion
Thus, the total number of different teams that can be selected is 256.
This matches option B.
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A team of 3 students is to be selected out of 4 study groups, each study group containing 4 students. What is the number of different teams that can be selected if more than one student cannot be selected from a study group?a)24b)256c)536d)544e)1536Correct answer is option 'B'. Can you explain this answer?
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