Uploaded by Sejaferavideos on 22.07.2007

Transcript:

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!

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!