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How many necklaces can be made using at least 5 from 8 beads of different colours?
- a)230
- b)2952
- c)5904
- d)7695
- e)5130
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
How many necklaces can be made using at least 5 from 8 beads of differ...
To solve this problem, we need to use the concept of combinations.
Combination Formula:
The number of combinations of selecting r objects from a set of n objects is given by the formula: nCr = n! / (r!(n-r)!), where n! represents the factorial of n.
In this case, we have 8 beads of different colors, and we need to make necklaces using at least 5 beads. This means we can choose 5, 6, 7, or 8 beads.
Case 1: Choosing 5 beads:
The number of ways to choose 5 beads from 8 beads is given by 8C5 = 8! / (5!(8-5)!) = 8! / (5!3!) = (8 * 7 * 6) / (3 * 2 * 1) = 56.
Case 2: Choosing 6 beads:
The number of ways to choose 6 beads from 8 beads is given by 8C6 = 8! / (6!(8-6)!) = 8! / (6!2!) = (8 * 7) / (2 * 1) = 28.
Case 3: Choosing 7 beads:
The number of ways to choose 7 beads from 8 beads is given by 8C7 = 8! / (7!(8-7)!) = 8! / (7!1!) = 8 / 1 = 8.
Case 4: Choosing 8 beads:
The number of ways to choose all 8 beads from 8 beads is given by 8C8 = 8! / (8!(8-8)!) = 8! / (8!0!) = 1.
Total number of necklaces:
To get the total number of necklaces, we need to sum up the number of combinations from all the cases:
56 + 28 + 8 + 1 = 93.
Therefore, the correct answer is option 'B' which is 93.
Combination Formula:
The number of combinations of selecting r objects from a set of n objects is given by the formula: nCr = n! / (r!(n-r)!), where n! represents the factorial of n.
In this case, we have 8 beads of different colors, and we need to make necklaces using at least 5 beads. This means we can choose 5, 6, 7, or 8 beads.
Case 1: Choosing 5 beads:
The number of ways to choose 5 beads from 8 beads is given by 8C5 = 8! / (5!(8-5)!) = 8! / (5!3!) = (8 * 7 * 6) / (3 * 2 * 1) = 56.
Case 2: Choosing 6 beads:
The number of ways to choose 6 beads from 8 beads is given by 8C6 = 8! / (6!(8-6)!) = 8! / (6!2!) = (8 * 7) / (2 * 1) = 28.
Case 3: Choosing 7 beads:
The number of ways to choose 7 beads from 8 beads is given by 8C7 = 8! / (7!(8-7)!) = 8! / (7!1!) = 8 / 1 = 8.
Case 4: Choosing 8 beads:
The number of ways to choose all 8 beads from 8 beads is given by 8C8 = 8! / (8!(8-8)!) = 8! / (8!0!) = 1.
Total number of necklaces:
To get the total number of necklaces, we need to sum up the number of combinations from all the cases:
56 + 28 + 8 + 1 = 93.
Therefore, the correct answer is option 'B' which is 93.
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Community Answer
How many necklaces can be made using at least 5 from 8 beads of differ...
The correct answer is 2952 .
the solution is simple !!!
At least 5 from 8 means we have 5,6,7, and 8.
for necklace or circle we take (n-1)!, then
4!+5!+6!+7!= 5904.
For necklace we have pairs (mirror), so we divide on 2.
5904/2= 2952
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How many necklaces can be made using at least 5 from 8 beads of different colours?a)230b)2952c)5904d)7695e)5130Correct answer is option 'B'. Can you explain this answer? for GRE 2025 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about How many necklaces can be made using at least 5 from 8 beads of different colours?a)230b)2952c)5904d)7695e)5130Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GRE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many necklaces can be made using at least 5 from 8 beads of different colours?a)230b)2952c)5904d)7695e)5130Correct answer is option 'B'. Can you explain this answer?.
How many necklaces can be made using at least 5 from 8 beads of different colours?a)230b)2952c)5904d)7695e)5130Correct answer is option 'B'. Can you explain this answer? for GRE 2025 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about How many necklaces can be made using at least 5 from 8 beads of different colours?a)230b)2952c)5904d)7695e)5130Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GRE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many necklaces can be made using at least 5 from 8 beads of different colours?a)230b)2952c)5904d)7695e)5130Correct answer is option 'B'. Can you explain this answer?.
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