Use 0,1,2,3,4 to form a three digit number 10 that does not repeat numbers

1) Because the hundred can only be selected in the inside, after the selection of the hundred, there are 4 choices for the single digit, and there are only 3 choices for the ten digits, if the single digit is 1, then the three-digit number has 4*3=12, and in the same way, the three-digit number of the single digit also has 12 respectively.

Therefore, the sum of single digits (0+1+2+3+4)x12=1202) is the same as above.

The sum of the hundred digits (1 + 2 + 3 + 4) x 12 = 120 is a little different than the ten digits, the first ten digits are selected, then there are 5 choices, then when the ten digits are , there are only 3 choices for the hundreds, and there are 3 choices for the single digit (optional 0), so there are 36 three-digit numbers. When the ten digit is 0, it is not considered (0 x any number = 0).

So the sum of the ten digits (1+2+3+4) x3x3=90 then the sum of all three digits is calculated as: hundred-digit sum x100 + ten-digit sum x10+ single digit.

120x100+90x10+120=13020

Solution: (1) 4 4 3 = 48

0+1+2+3+4）x12=120

2) 120x100 + 90x10 + 120 = 13020 Answer: (1) The sum of the single digits of all three digits is 120.

2) The sum of all three digits is 13020.

24 species. With the step-by-step method, the number of hundreds will not be 0, so there are 4 kinds, and the single digit and the ten digit are the combination of the remaining 4 and choose 2 (it is a combination not a permutation, such as 21 and 12 are repeated numbers), so it is 4 * 3 2 = 6 kinds.

A total of 4*6=24 species.

Two commonly used permutations: basic counting principles and applications.

1. Addition principle and categorical counting method:

Each of the methods in each class can accomplish this task independently; The specific methods in the two different types of approaches are different from each other (i.e., the classification is not duplicated); Any way to accomplish this task belongs to a certain category (i.e., classification is not missing).

2. Multiplication principle and step-by-step counting method:

None of the methods of any step can complete this task, and this task must be completed only if these n steps are completed consecutively; Each step counts independently of each other; As long as there is a different method taken in one step, the corresponding method of accomplishing the matter is also different.

First of all, choose the number on the hundred, there are 4 ways to choose the hundred, secondly, choose the number on the ten place, there are 4 ways to choose, and there are only 3 ways to choose on the single place, so 0, 1, 2, 3, 4 can form 4 * 4 * 3 = 48 numbers without repeating three digits.

Solution: Start with the hundreds, the hundreds, the hundreds, there are 4 ways to choose the ten digits to remove the hundreds, choose one from the remaining 4 numbers, and there are also 4 ways to choose one of the remaining 3 numbers in the single digits, there are 3 choices.

So there are 4x4x3 = 48 different digits that are not repeated.

1. Use each only once: (24+24=48).

Contains 0: c(4,2)*c(2,1)*p(2,2)=24, does not contain 0:c(4,3)*p(3,3)=24

2. One of the numbers is used twice :(8+4+18=30) with 0: (1)0 once: c(4,1)*c(2,1)=8(2)0 twice: c(4,1)=4

Without 0: c(4,2)*c(3,1)=18

3. One of the numbers is used 3 times: (3).

c(4,3)=3

So the total: 48 + 30 + 3 = 81

Take any 3 of the 5 numbers - the number with the first 0.

p(5,3)-p(4,2)=60-12=48

If you don't consider 0 in the three-digit number, it is 4*3*2, but in this case there is the possibility of 0 in the first place, all when 0 is in the first place (hundred), then the selection of the single digit and the ten digit has 3*2, that is, removing the 0 in the first place may be 4! -3！

Solution: p5(3)=4x5x5=100 (pcs).

A: The numbers 0, 1, 2, 3, and 4 can be used to form 100 different three-digit numbers.

Because 0 can't be in the highest position.

So there are 3 options on the hundreds.

There are 3 choices in the 10th place (100 uses a number).

There are 2 options in the single digit (2 for the 100 and 10 digits).

So in total: 3 3 2 = 18 species.

Although the result is the same.

But that's not rigorous.

This answer should be a four-digit answer without repeating the number.

It should be A43-A32

It's 4x3x2-3x2

I don't play permutated symbols.

It means that 3 of the 4 numbers are arranged arbitrarily.

But since 0 cannot be a hundred.

So minus. a32 is 1

23. The three numbers are all arranged in any two of them.

by the number 012

How many three-digit numbers can be made up of 34:

The hundredth digit of this three-digit number can only be these four, and there are 5 kinds of ten digits and single digits, so there are 4*5*5=100.

by the number 012

34 can make up how many triple digits without repeating numbers.

The hundredth digit of this three-digit number can only be these four, and the number on the ten digit is 012

One of the remaining 4 numbers in 34, there are 4 kinds.

The number in the single digit is 012

One of the remaining 3 numbers in 34, there are 3 kinds.

So there are 4*4*3=48.

4*4*3=48 species.

It can't be 0 in the hundreds, so there are 4 options; Then there is no restriction on the tens digits, and after removing the number on the hundreds, there are 4 options; In the single digit, remove the number on the 100 and 10 digits, and there are 3 options.

It's ......Math problems.

Hundreds can only

1 out of 4 out of 10 out of 3 out of 1

c41*c41*c31=48

Or choose two out of ten or 4 digits.

First of all, choose the number on the hundred, there are 4 kinds of auspicious imitation of the fiber selection method on the hundred, secondly, choose the number on the ten place, there are 4 kinds of selection, and there are only 3 ways to choose the early front of the single digit, so 0, 1, 2, 3, 4 can form 4 * 4 * 3 = 48 numbers do not repeat the three digits.

Three-digit numbers starting with 4: 402,420;

Three-digit numbers starting with 2: 204,240;

Therefore, the three numbers 4, 0, and 2 can make up 4 different three-digit numbers, so the answer is: 4

Because the highest digit cannot be 0, so the number on the hundred digit can only be 2, 3, 4, there are three cases, and the number on the ten digit is any one of the remaining three numbers, so there are also three cases, and the number on the single digit is any of the remaining two numbers, so there are two cases, then there can be a three-digit number that can be composed of: 3 3 2 = 18 kinds.

These 18 are:

This three-digit number has three possibilities: 1, 2, and 3 in the hundred.

In addition to the number on the hundred, there are three possible numbers in the ten place, and there are also three possible numbers.

In addition to the number in the hundred and ten places, there are two possibilities, so 3*3*2=18 can be used to form 18 three-digit numbers without repeating numbers.

According to the principle of multiplication, it can be obtained:

3 3 2=18 (pcs);

Answer: There are 18 four-digit numbers that can be composed of 0, 1, 2, and 3 without repeating numbers

Use to form four digits with (18) numbers that are not repeated.