Understanding Permutations For Class 12 Smk Students
Understanding Permutations for Class 12 SMK Students
What is a Permutation?
A permutation is a rearrangement of a set of items. It is an ordered sequence of elements from a given set. Commonly, permutations are used to solve mathematical problems. In class 12 SMK, students are taught about permutations and its application in solving mathematical problems.
Example of Permutation
Let us take an example of permutation with 3 letters: A, B and C. The possible permutations are: ABC, ACB, BAC, BCA, CAB and CBA. Here, the order of the letters is important. If we take the permutation ABC then A should come first, followed by B and then C.
Types of Permutation
There are two types of permutations - circular permutations and non-circular permutations. Circular permutations are those where the arrangement of the elements is circular in nature. For example, ABC, CAB and BCA are some examples of circular permutations. Non-circular permutations are those where the arrangement of the elements is not circular in nature. For example, ACB and BAC are some examples of non-circular permutations.
Calculating Permutations
The number of permutations in a set of n elements can be calculated using the formula nP r = n!/(n-r)!. Here, n is the number of elements in the set and r is the number of elements to be chosen. For example, if we have a set of 3 elements, then the number of permutations is 3P 3 = 3!/(3-3)! = 3! / 0! = 3! = 6.
Permutation Problems
Permutations are often used to solve mathematical problems. For example, let us take a problem where a group of 4 students needs to arrange themselves in a line. Here, the order of the students is important. The number of possible permutations is 4P 4 = 4! / (4-4)! = 4! / 0! = 4! = 24.
Permutations and Combinations
Permutations and combinations are often confused with each other. However, there is a difference between them. Permutations are rearrangements of a set of elements and the order of the elements is important. On the other hand, combinations are selections of a set of elements and the order of the elements is not important.
Examples of Permutations in Class 12 SMK
Class 12 SMK students are taught about permutations and its application in solving mathematical problems. Some examples of problems that can be solved using permutations are: finding the number of possible arrangements of 4 students in a line, finding the number of possible words that can be formed using the letters of the word ‘MATHEMATICS’, finding the number of possible ways to arrange the letters of the word ‘EXAMINATION’, etc.
Conclusion
Permutations are rearrangements of a set of elements and the order of the elements is important. It is an important topic that is taught to Class 12 SMK students and it has numerous applications in solving mathematical problems.
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