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Permutation of Distinct and Non-Distinct Objects

5 Questions

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Permutation of Distinct and Non-Distinct Objects

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Questions and Answers

What is the total number of permutations for 5 distinct objects?

120 (correct)

100

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?

10 (correct)

What is the value of $4!$?

<p>24</p> Signup and view all the answers

How is the total number of permutations of 6 objects with 2 of type A and 4 of type B calculated?

<p>$rac{6!}{2! imes 4!}$</p> Signup and view all the answers

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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Description

This quiz explores the concepts of permutations for both distinct and non-distinct objects, emphasizing the use of factorial calculations. It provides examples to illustrate how various arrangement scenarios can be computed, helping learners grasp the underlying principles of permutation effectively.