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In how many ways 5 African and five Indian can be seated along a circular table, so that they occupy alternate position.
- a)5! 5!
- b)4! 5!
- c)5! 4!
- d)4! 4!
Correct answer is option 'B'. Can you explain this answer?
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In how many ways 5 African and five Indian can be seated along a circu...
Answer – b) 4! 5!
Explanation : First 5 African are seated along the circular table in (5-1)! Ways = 4!. Now Indian can be seated in 5! Ways, so 4! 5!
Explanation : First 5 African are seated along the circular table in (5-1)! Ways = 4!. Now Indian can be seated in 5! Ways, so 4! 5!
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In how many ways 5 African and five Indian can be seated along a circu...
Solution:
To solve this problem, we need to consider that the Indian and African people are seated alternately. Therefore, we can assume that there are two groups, one consisting of the Indian people and one consisting of the African people. Thus, we can arrange the Indian group and African group separately and then combine them.
1. Arrangement of Indian Group:
The Indian group consists of five people, and they can be arranged in a circular table in (4!) ways because we can fix one person at one point and then arrange the rest of them in a circular permutation. Therefore, the number of ways to arrange Indian Group is 4!.
2. Arrangement of African Group:
Similarly, the African group consists of five people, and they can be arranged in a circular table in (5!) ways because we can fix one person at one point, and then arrange the rest of them in a circular permutation. Therefore, the number of ways to arrange African Group is 5!.
3. Combining the Groups:
Since the Indian and African people are seated alternately, we need to multiply the two arrangements to obtain the final answer. Therefore, the total number of ways to seat five African and five Indian people alternately is given by:
4! × 5! = 24 × 120 = 2,880
Thus, the correct option is B. 4! × 5!.
To solve this problem, we need to consider that the Indian and African people are seated alternately. Therefore, we can assume that there are two groups, one consisting of the Indian people and one consisting of the African people. Thus, we can arrange the Indian group and African group separately and then combine them.
1. Arrangement of Indian Group:
The Indian group consists of five people, and they can be arranged in a circular table in (4!) ways because we can fix one person at one point and then arrange the rest of them in a circular permutation. Therefore, the number of ways to arrange Indian Group is 4!.
2. Arrangement of African Group:
Similarly, the African group consists of five people, and they can be arranged in a circular table in (5!) ways because we can fix one person at one point, and then arrange the rest of them in a circular permutation. Therefore, the number of ways to arrange African Group is 5!.
3. Combining the Groups:
Since the Indian and African people are seated alternately, we need to multiply the two arrangements to obtain the final answer. Therefore, the total number of ways to seat five African and five Indian people alternately is given by:
4! × 5! = 24 × 120 = 2,880
Thus, the correct option is B. 4! × 5!.
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In how many ways 5 African and five Indian can be seated along a circu...
Answer – b) 4! 5!
Explanation : First 5 African are seated along the circular table in (5-1)! Ways = 4!. Now Indian can be seated in 5! Ways, so 4! 5!
Explanation : First 5 African are seated along the circular table in (5-1)! Ways = 4!. Now Indian can be seated in 5! Ways, so 4! 5!
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In how many ways 5 African and five Indian can be seated along a circular table, so that they occupy alternate position.a)5! 5!b)4! 5!c)5! 4!d)4! 4!Correct answer is option 'B'. Can you explain this answer?
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