Basic knowledge of permutation and combination
1 addition principle: There are n ways to do one thing. There are two ways in the first category, two ways in the second category and three ways in the n category, so there are * * * different ways to accomplish this.
2 multiplication principle: to do one thing, it needs to be divided into n steps. There is a way to do the first step and a way to do the second step.
3 permutation number formula:
Full permutation formula:
4 combination number formula:
Two property theorems of combinatorial numbers;
( 1)
(2)
Addition principle's emphasis is on the word "class" and the principle of multiplication is on the word "step". When applying addition principle, we should pay attention to the independence and juxtaposition between "class" and "class", which are both independent and juxtaposed in various methods. When applying the principle of multiplication, we should pay attention to the continuity between "step" and "step". Doing one thing needs to be divided into several steps, completed step by step, and finally completed the whole work.
6 Arrangement and combination are two different but related concepts. Their similarity is "choose any M elements from N different elements", but the difference is that the former should be arranged in a column according to a certain order, while the latter is "combined into a group without order". Therefore, when dealing with specific problems, we should grasp the key of "order" to distinguish the problems of permutation and combination.
Senior one 1 Class (1) organized students to participate in two extracurricular activities, namely, math group activities and English group activities. Among them, 12 people took part in math group activities, 24 people took part in English group activities, and 8 people took part in both activities, so there are _ _ _ _ _ _ people in this class. P3
2. Choose two numbers (repeatable) from 1 to 6. There are _ _ _ _ _ _ * cases where the difference between the two numbers is even. P 10
3. From 1000 to 2000, there are _ _ _ _ _ _ positive integers with thousands less than hundreds, hundreds less than tens, and tens less than single digits. P 1 1
4. Choose three numbers from 1, 3, 5, 7 and 9, and two numbers from 0, 2, 4, 6 and 8 to form _ _ _ _ _ different five-digit numbers. P 12
5. Of all the four digits, the sum of _ _ _ _ _ _ _ digits is equal to 34. P 17
6. The sum of seven digits is 60, and such seven digits are _ _ _ _ _ _ _. P 17
7. Among the positive integers less than 10000, there are _ _ _ _ _ _ _ numbers added to 2374 at least once. P 17
8. There are four extracurricular groups: calligraphy, dance, football and mathematics in the first grade of junior high school in a school. There are 46 students in a class, each of whom participates in at least one group and at most three groups. Then, at least _ _ _ _ _ _ students join the same extracurricular group. P34
9. What is the unit number of the product? p 1
The product of 10 and three prime factors is exactly equal to 1 1 times of their sum, so what are these three prime numbers respectively? p2
1 1, if the equation, then how many integer solutions does this equation * * * have? p2
12 has a four-digit number, the first digit is the smallest, the second digit is the largest, and the third digit is equal to twice the sum of the first two digits. How many such four digits are there? p 1 1
13, Party A, Party B, Party D and Xiao Li play table tennis, and every two people have to play a game. So far, Party A has played 4 games, Party B has played 3 games, Party C has played 2 games, and Party D has only played 1 game. So how many games did Xiao Li play? p 16
14. There are five cards with numbers on them: 1, 2, 0, 0, 3. They can form many different five-digit numbers. What is the average of these five figures? p 16
15. If there is a four-digit number, its ten digits are less than one digit 1, and one digit is less than one hundred digits 1. The sum of it and its reciprocal (such as 1234 and 432 1) is10766. p 17
16, there are several table tennis teams *** 10 players. If there are games between players from different teams and there are no games between players from the same team, then one * * * will have 27 games, and then there will be a team with two players. P25
17. If the simplification result of algebraic expression is 2a, then mark the corresponding positions of A, B and C on the number axis. P25
18, a six-digit number is a multiple of 4, divided by 5 is 1 1, and the middle four digits are 1527, so the sum of the first and last digits is. p3 1