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In a class 6 students have to be arranged for a photograph. If the prefect and the vice must occupy the positions at either ends, how many ways the students can be arranged?
- a)58
- b)48
- c)64
- d)32
Correct answer is option 'B'. Can you explain this answer?
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In a class 6 students have to be arranged for a photograph. If the pre...
In a class of 6 students. Two students at both ends. Remaining four students have to be arranged
= 2 * 4!
= 2 * 24
= 48
= 2 * 4!
= 2 * 24
= 48
Most Upvoted Answer
In a class 6 students have to be arranged for a photograph. If the pre...
2students at both ends =24 students in between= 4!students can be arranged in 4!*2= 48 ways..
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In a class 6 students have to be arranged for a photograph. If the pre...
Solution:
To solve this problem, we can consider the positions of the prefect and vice-prefect fixed at the ends. This means that the remaining 4 students can be arranged in the middle positions.
1. Positions of the prefect and vice-prefect:
- The prefect can be placed at one end in 1 way.
- The vice-prefect can be placed at the other end in 1 way.
2. Arrangement of the remaining 4 students:
- Once the prefect and vice-prefect are placed, the remaining 4 students can be arranged in the middle positions in 4! = 4 × 3 × 2 × 1 = 24 ways.
(Here, 4! denotes the factorial of 4, which is the number of ways to arrange 4 distinct objects.)
3. Total number of arrangements:
- The positions of the prefect and vice-prefect are fixed, so the number of total arrangements is the product of the number of ways to arrange the prefect and vice-prefect and the number of ways to arrange the remaining 4 students.
- Total number of arrangements = 1 × 1 × 4! = 24.
Therefore, the correct answer is option B: 48.
To solve this problem, we can consider the positions of the prefect and vice-prefect fixed at the ends. This means that the remaining 4 students can be arranged in the middle positions.
1. Positions of the prefect and vice-prefect:
- The prefect can be placed at one end in 1 way.
- The vice-prefect can be placed at the other end in 1 way.
2. Arrangement of the remaining 4 students:
- Once the prefect and vice-prefect are placed, the remaining 4 students can be arranged in the middle positions in 4! = 4 × 3 × 2 × 1 = 24 ways.
(Here, 4! denotes the factorial of 4, which is the number of ways to arrange 4 distinct objects.)
3. Total number of arrangements:
- The positions of the prefect and vice-prefect are fixed, so the number of total arrangements is the product of the number of ways to arrange the prefect and vice-prefect and the number of ways to arrange the remaining 4 students.
- Total number of arrangements = 1 × 1 × 4! = 24.
Therefore, the correct answer is option B: 48.
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In a class 6 students have to be arranged for a photograph. If the prefect and the vice must occupy the positions at either ends, how many ways the students can be arranged?a)58b)48c)64d)32Correct answer is option 'B'. Can you explain this answer?
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