Hello, in today's lesson we will see it combinatorial analysis
In this issue we are concerned with problems of counting
Thus our question is; How many? How many? What?
How many rows? How many ways can distribute some objects to some people?
In this matter there are several myths, however it is a very simple
The first human intellectual activity is to objects. Since early learn to count
In this lesson inumeras learn techniques for counting.
To resolve issues of competition and vestibular
The first technique that must dominate in combinatorial is:
When you add? and When you multiply?
There is a hint:
That results in combinatorial if we divide the issues in cases
That is the question will be divided into cases.
Appears the idea of "or" exclusive. You will do something "or" other never both at the same time.
And when multiply results in combinatorial?
When making decisions in sequence or making decisions consecutive
So multiply the results It appears the idea of the "and"
Since "and" reminds consecutive
The sum, in combination, is called Principle additive
The increase in combinatorial, is called multiplicative principle.
Consider the example of orange and tangerine.
Disposal of 4 oranges and 3 different sieves
Question: How many ways can I choose a fruit?
The answer is: How should I choose a single fruit should I divide my problem in cases
If choice 1 orange have 4 options to choose If choice 1 tangerine have 3 options
Thus, in total, will have 4 + 3 option. Note that the results somei
Sure, therefore, I choose "or" an orange "or" a tangerine.
If you have 4 oranges in one hand and 3 tinker with another.
I should add or multiply the quantities to know the total amount?
It seems obvious that the results add That is, we use the additive principle.
Next question: How many ways you can choose 1 orange and 1 tangerine?
What you should do now is take 2 DECISIONS IN SEQUENCE
that is, first you choose 1 tangerine orange and after 1 ...
First choose 1 orange decision: I have 4 options
The second decision: choose 1 tangerine I have 3 options distinct
How to make two decisions in sequence multiply the results.
So we have 4 times 3 different ways choose from 1 orange and tangerine after 1
And note the showing. Remember?
Multiplicative principle
4 times 3 mean in 12 ways
Now I ask: Why are we allowed to multiply the results?
The idea is beautiful. The proliferation is a sum of equal installments. In other words, the increase stems from a sum.
If you divide the second problem in cases born a sum which results in simplified product. Amazing!
Suppose: You chose the orange 1.
After the choice of orange 1, is the second decision: 1 tangerine choose ...
You have 3 options: tangerine A, B or C
Each track represents a different action For example:
L1 is that Mc chose: orange 1 tangerine C
It will have 3 options
Imagine that instead of 1 orange you have chosen to orange 2.
The idea is similar: After choosing the orange 2
We have to choose 1 tangerine out of 3
It is 3 more options
doing the same for the orange 3 and 4
At the end we will have 4 cases of 3 options, note:
we will have 3 + 3 + 3 + 3 options
What is the sum of 4 plots of 3?
This results in 4 times 3
But 4 is precisely the number of oranges
So we are allowed to multiply
We will now learn how to train couples ...
To this have 5 women and 4 men
Question: How many ways can I make a couple?
However, to form a double what we have to do is
make two decisions in sequence
that is, choose 1 woman and 1 man soon after for the couple
1 woman choose to have 5 options
and 1 man have to choose 4 options
How to make two decisions in sequence Then choose woman man
We will multiply the results
Final answer: 5 times 4 results in 20 ways to form a couple
Thank you! Check out the class 2!
