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There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place?
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There are 10 friends A B C D E F G H I J they are supposed to sit in a...
Arranging Friends in a Line
1) Arrangement starting with A and ending with J:
To find the number of ways to arrange the friends in a line starting with A and ending with J, we can fix A and J in the first and last positions respectively. The remaining 8 friends (B, C, D, E, F, G, H, I) can be arranged in the remaining 8 positions.
To calculate the number of ways to arrange 8 friends in 8 positions, we use the concept of permutations. The number of permutations of n objects taken r at a time is given by nPr = n! / (n-r)!
In this case, n = 8 and r = 8. Therefore, the number of ways to arrange the remaining 8 friends is 8P8 = 8! / (8-8)! = 8! / 0! = 8!.
Hence, the total number of ways to arrange the friends in a line starting with A and ending with J is 8!.
2) Arrangement with A, B, C, D, E together and F, G, H, I, J together:
To find the number of ways to arrange the friends in a line with A, B, C, D, E together and F, G, H, I, J together, we can consider A, B, C, D, E as a single entity and F, G, H, I, J as another single entity. This reduces the problem to arranging two entities in a line.
The number of ways to arrange two entities in a line is 2!. However, within each entity, the friends can be arranged in different ways. For the first entity (A, B, C, D, E), there are 5! ways to arrange the friends. Similarly, for the second entity (F, G, H, I, J), there are 5! ways to arrange the friends.
Therefore, the total number of ways to arrange the friends in a line with A, B, C, D, E together and F, G, H, I, J together is 2! * 5! * 5! = 2 * 5! * 5!.
3) B always occupies an even place:
To find the number of ways to arrange the friends in a line where B always occupies an even place, we can fix B in one of the even positions. There are 5 even positions in a line of 10 friends (positions 2, 4, 6, 8, 10).
Once B is fixed in an even position, the remaining 9 friends can be arranged in the remaining 9 positions. Using the concept of permutations, the number of ways to arrange 9 friends in 9 positions is 9!.
Therefore, the total number of ways to arrange the friends in a line where B always occupies an even place is 5 * 9! = 5 * 9!.
1) Arrangement starting with A and ending with J:
To find the number of ways to arrange the friends in a line starting with A and ending with J, we can fix A and J in the first and last positions respectively. The remaining 8 friends (B, C, D, E, F, G, H, I) can be arranged in the remaining 8 positions.
To calculate the number of ways to arrange 8 friends in 8 positions, we use the concept of permutations. The number of permutations of n objects taken r at a time is given by nPr = n! / (n-r)!
In this case, n = 8 and r = 8. Therefore, the number of ways to arrange the remaining 8 friends is 8P8 = 8! / (8-8)! = 8! / 0! = 8!.
Hence, the total number of ways to arrange the friends in a line starting with A and ending with J is 8!.
2) Arrangement with A, B, C, D, E together and F, G, H, I, J together:
To find the number of ways to arrange the friends in a line with A, B, C, D, E together and F, G, H, I, J together, we can consider A, B, C, D, E as a single entity and F, G, H, I, J as another single entity. This reduces the problem to arranging two entities in a line.
The number of ways to arrange two entities in a line is 2!. However, within each entity, the friends can be arranged in different ways. For the first entity (A, B, C, D, E), there are 5! ways to arrange the friends. Similarly, for the second entity (F, G, H, I, J), there are 5! ways to arrange the friends.
Therefore, the total number of ways to arrange the friends in a line with A, B, C, D, E together and F, G, H, I, J together is 2! * 5! * 5! = 2 * 5! * 5!.
3) B always occupies an even place:
To find the number of ways to arrange the friends in a line where B always occupies an even place, we can fix B in one of the even positions. There are 5 even positions in a line of 10 friends (positions 2, 4, 6, 8, 10).
Once B is fixed in an even position, the remaining 9 friends can be arranged in the remaining 9 positions. Using the concept of permutations, the number of ways to arrange 9 friends in 9 positions is 9!.
Therefore, the total number of ways to arrange the friends in a line where B always occupies an even place is 5 * 9! = 5 * 9!.
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There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place?
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There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place?.
There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 10 friends A B C D E F G H I J they are supposed to sit in a line find the number of ways 1) if sitting arrangement starts with A and ends with J 2) if A B C D E will sit together and F G H I J will sit together 3)if B always occupy even place?.
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