Explanation of Differences of Permutations and Combinations of Mathematics, Examples of Problems and Complete Discussion

Permutations and Combinations of Mathematics - Math lessons on permutations and combinations are taught to students who are in high school XI. This material is still related to Opportunities. So what's the difference between chance, permutation and combination? Relax, do not hurry. In this article The Basic Mathematical Formula will describe one by one to you about permutations and combinations in mathematics. As for the material opportunities you can access on the article that discusses Definition and Formulas of Opportunities Mathematics .


As always, here you are not only getting material explanations but also formulas As well as examples of problems and explanations of the steps in answering the question. Therefore, you should pay attention to both the description of the material and the explanation of the given formula.
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Definition of Permutations and Combinations of Mathematics


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Permutation

In the science of mathematics a permutation is defined as a concept of composing a set of objects / numbers into multiple Different sequences without repetition.

In the permutation, the sequence is heavily addressed. Each resulting object must be different from one to another. We take for example, the order of letters (ABC is different from CAB as well as {BAC) and ACB). The formula for finding the number of permutations n elements when composed on elements k d i where k N is:

The formula of permutation

P (n, k) = n!
(nk)!

To understand the formula, consider the following discussion:


Sample Problem 1
In a school there are 4 teachers who are nominated to fill the position of treasurer and secretary. Try to find out how many ways you can fill that position!

Discussion :
The above problem can be written as permutation P (4.2), n (number of teachers) = 4 k (number of positions) = 2
enter into the formula:

P (4,2) = 4! [1945909] = 4 x 3 x 2 x 1 = 24 = 12
(4-2)! 2 x 1 2


Sample Problem 2
How many numbers are formed from 2 different numbers that we can construct from the order of the numbers 4, (19459015) Discussion:
The above question can be concluded as a permutation consisting of 2 elements selected from 5 elements it can be written as P (5,2). Live we enter into the formula.

P (5,2) = 5! [194590]] 120 = 20
(5-2 )! 3 x 2 x 1 6

Then there are 20 ways that can be done to synthesize these numbers into 2 different numbers (48 , 42, 43, 45, 84, 82, 83, 85, 53, 52, 52, 52, 52, 52).

Combination

combinations are a collection of some or all of the objects with no regard to their order. In combination, AB is considered to be the same as BA so that a combination of two identical objects can not be repeated.

The formula of combinations of a set having n elements can be written as follows:

[1945907] Combination formula

C ( n , R ) = n C r = n C r = n!
r! (Nr)!

Let us observe the use of the formula to solve the following problems:


Sample Problem 3
Manuel Pelegrini brought 16 players at Manchester City against Liverpool at Etihad Stadium. 11 of them will be selected to play in the first half. If we do not pay attention to the player's position, how many ways can the coach take to choose a player?

Discussion:
Emphasizing the player's position, then we use the combination formula:
16 C 11 = 16! [194590]] 16 x 15 x 14 x 13 x 12 x 11!
11! (16-11)! 11! 5!

= 524160 =
5 x 4 x 3 x 2 x 1 120


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Example Problem 4

A bucket containing 1 avocado, 1 pear, 1 orange and 1 salak. How many combinations are composed of three kinds of fruit?
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Discussion:
known n = 4 and R = 3, then:

4 C 3 = 4! 24 = 4
3! (4-3)! 3! 1! 3 x 2 x 1 6


Okay, now you must have understood about here before the discussion of material Differences in Permutations and Combinations of Mathematics, Sample Problems and Complete Discussion for this occasion. Please refer to other mathematics lesson material in this blog to increase your knowledge about mathematics.
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