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Questions and Answers
What is the total number of permutations for 5 distinct objects?
What is the total number of permutations for 5 distinct objects?
- 60
- 24
- 120 (correct)
- 100
Which formula correctly represents the permutation of non-distinct objects?
Which formula correctly represents the permutation of non-distinct objects?
- $n!$
- $ rac{n!}{n_1! imes n_2! imes n_3!}$ (correct)
- $ rac{n!}{n!}$
- $ rac{n}{n_1! imes n_2!}$
If there are 3 objects of type A and 2 objects of type B, how many distinct permutations can be formed?
If there are 3 objects of type A and 2 objects of type B, how many distinct permutations can be formed?
- 15
- 5
- 8
- 10 (correct)
What is the value of $4!$?
What is the value of $4!$?
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How is the total number of permutations of 6 objects with 2 of type A and 4 of type B calculated?
How is the total number of permutations of 6 objects with 2 of type A and 4 of type B calculated?
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Study Notes
Permutation of Distinct Objects
- Calculating the number of possible arrangements for a set of distinct objects uses the factorial function.
- The factorial function, denoted as 'n!', represents the product of all positive integers less than or equal to 'n'.
- For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
- This means there are 120 different ways to arrange 5 distinct objects.
Permutation of Non-Distinct Objects
- When dealing with non-distinct objects, the calculation involves dividing the factorial of the total number of objects by the factorial of the number of repetitions for each type of object.
- This accounts for the repetitions and avoids overcounting arrangements.
- For instance, having 5 objects with 2 of type A and 3 of type B, the formula becomes 5!/(2! * 3!), resulting in 10 unique arrangements.
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