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In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated?
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In how many ways 8 stones of different colours be arranged on a ring? ...
Arranging 8 stones on a ring:
To find the number of ways to arrange 8 stones of different colors on a ring, we can use the concept of circular permutations. Circular permutations are arrangements where the order of objects matters, but the starting point is not fixed.
The number of ways to arrange n objects in a circle is given by (n-1)!. In this case, we have 8 stones, so the number of arrangements is (8-1)! = 7!.
Therefore, there are 7! = 5040 ways to arrange 8 stones of different colors on a ring.
Arranging red and yellow beads separately:
To find the number of arrangements where the red and yellow beads are separated, we can consider them as a single unit. Let's call this unit "RY".
Now, we have 7 objects to arrange on the ring - RY, plus 6 other stones. The number of arrangements of these 7 objects can be found using circular permutations, which is (7-1)! = 6!.
But within the RY unit, the red and yellow beads can be arranged in 2! = 2 ways.
Therefore, the number of arrangements where the red and yellow beads are separated is 6! * 2 = 720.
Explanation:
1. Arranging 8 stones on a ring:
- To find the number of ways to arrange 8 stones of different colors on a ring, we use the concept of circular permutations.
- Circular permutations consider the order of objects but not the starting point.
- The formula for circular permutations is (n-1)!, where n is the number of objects.
- In this case, we have 8 stones, so the number of arrangements is (8-1)! = 7! = 5040.
2. Arranging red and yellow beads separately:
- To find the number of arrangements where the red and yellow beads are separated, we consider them as a single unit called RY.
- Now, we have 7 objects to arrange on the ring - RY and 6 other stones.
- The number of arrangements of these 7 objects can be found using circular permutations, which is (7-1)! = 6! = 720.
- But within the RY unit, the red and yellow beads can be arranged in 2! = 2 ways.
- Therefore, the number of arrangements where the red and yellow beads are separated is 6! * 2 = 720.
To find the number of ways to arrange 8 stones of different colors on a ring, we can use the concept of circular permutations. Circular permutations are arrangements where the order of objects matters, but the starting point is not fixed.
The number of ways to arrange n objects in a circle is given by (n-1)!. In this case, we have 8 stones, so the number of arrangements is (8-1)! = 7!.
Therefore, there are 7! = 5040 ways to arrange 8 stones of different colors on a ring.
Arranging red and yellow beads separately:
To find the number of arrangements where the red and yellow beads are separated, we can consider them as a single unit. Let's call this unit "RY".
Now, we have 7 objects to arrange on the ring - RY, plus 6 other stones. The number of arrangements of these 7 objects can be found using circular permutations, which is (7-1)! = 6!.
But within the RY unit, the red and yellow beads can be arranged in 2! = 2 ways.
Therefore, the number of arrangements where the red and yellow beads are separated is 6! * 2 = 720.
Explanation:
1. Arranging 8 stones on a ring:
- To find the number of ways to arrange 8 stones of different colors on a ring, we use the concept of circular permutations.
- Circular permutations consider the order of objects but not the starting point.
- The formula for circular permutations is (n-1)!, where n is the number of objects.
- In this case, we have 8 stones, so the number of arrangements is (8-1)! = 7! = 5040.
2. Arranging red and yellow beads separately:
- To find the number of arrangements where the red and yellow beads are separated, we consider them as a single unit called RY.
- Now, we have 7 objects to arrange on the ring - RY and 6 other stones.
- The number of arrangements of these 7 objects can be found using circular permutations, which is (7-1)! = 6! = 720.
- But within the RY unit, the red and yellow beads can be arranged in 2! = 2 ways.
- Therefore, the number of arrangements where the red and yellow beads are separated is 6! * 2 = 720.
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In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated?
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In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated?.
In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways 8 stones of different colours be arranged on a ring? In how many of these arrangements red and yellow beads being separated?.
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