An Introduction To Permutations Of Equal Elements
An Introduction to Permutations of Equal Elements
If you’ve ever studied mathematics, you may have come across permutations. Permutations are a way of arranging a set of elements in a particular order. Permutations of equal elements are a type of permutations that involve arranging a set of identical elements in different ways.
What is a Permutation of Equal Elements?
A permutation of equal elements is a mathematical way of arranging a set of identical elements in different ways. For example, if you have a set of three identical elements, say a, b, and c, you could arrange them in the following ways: abc, acb, bac, bca, cab, and cba.
Types of Permutations
There are two different types of permutations: permutations with repetition and permutations without repetition. Permutations with repetition involve arranging a set of identical elements in different ways, but the same element can appear more than once in the set. For example, if you have three identical elements, say a, b, and c, you could arrange them in the following ways: aaa, aab, aba, baa, abb, bba, bcb, cbc, ccc.
Permutations without repetition involve arranging a set of identical elements in different ways, but each element can only appear once in the set. For example, if you have three identical elements, say a, b, and c, you could arrange them in the following ways: abc, acb, bac, bca, cab, and cba.
Example of a Permutation with Equal Elements
Let’s take a look at a simple example of a permutation with equal elements. Say you have three identical elements, a, b, and c. You could arrange them in the following ways: abc, acb, bac, bca, cab, and cba.
How to Calculate Permutations with Equal Elements
The formula for calculating permutations with equal elements is n!, where n is the number of elements in the set. For example, if you have three elements in the set, the formula would be 3!. This would give you 6 different permutations (abc, acb, bac, bca, cab, and cba).
How to Solve Permutations of Equal Elements
When it comes to solving permutations of equal elements, there are a few different methods you can use. The most common method is to use the formula n!, as mentioned previously. However, you can also use a method called ‘trial and error’. This involves trying out different combinations of elements until you find the right one.
Contoh Soal Permutasi Unsur Yang Sama
Berikut ini adalah contoh soal permutasi unsur yang sama:
Ani memiliki 3 buah bola merah, 3 buah bola biru, dan 3 buah bola hijau. Berapa rombakan warna bola yang bisa dibuat oleh Ani?
Jawabannya adalah 6 rombakan warna bola. Ini karena permutasi unsur yang sama dengan 3 unsur adalah 3! = 6.
Conclusion
In summary, permutations of equal elements involve arranging a set of identical elements in different ways. There are two types of permutations: permutations with repetition and permutations without repetition. The formula for calculating permutations with equal elements is n!, where n is the number of elements in the set. Lastly, you can use a method called ‘trial and error’ to solve permutations of equal elements.
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