Lecture 4 Enumeration 1

Content overview

Master the general method of enumeration. Learn to list them in a certain order and regularly, so as to achieve "neither weight nor leakage"; Solving the problem of integer segmentation by dictionary arrangement. Learn to distinguish between "counting order" and "out of order"

Interesting articles

1.？ Dongdong drew some numbers on a piece of paper, as shown in the picture. Each figure consists of several line segments. Please count how many line segments are there on a piece of paper. (The outermost large rectangular border, not counting)

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Analysis: 24 articles

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2.？ How many different ways can western Europe take from point A to point B along the road shown in the picture, and each section can only pass once at most?

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Analysis: 4 kinds

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3.？ Xiaoming decided to travel to Xiangshan, Summer Palace and Yuanmingyuan. How many different tour orders does he have for these three scenic spots?

Analysis: 6 kinds

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4.？ Xiao Wang is going to choose two places to travel from Qingdao, Sanya, Guilin and Hangzhou. How many different ways did Xiao Wang choose? If Xiao Wang wants to go to these three places, how many choices do he have?

Analysis: 6 kinds; four fundamental arithmetic operations

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5.？ Small biscuits are fifty cents each, and big biscuits are 2 yuan dollars each. DongDongYi * * has 6 yuan money. If all this money is used to buy baked wheat cakes, how many different ways can Dong Yi * * buy them?

Analysis: 4 kinds

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6.？ In a knowledge contest, Xiaoyue and Dongdong answered correctly 10 questions, and everyone had correct questions. If each question is 1, how many points might Abortion and Dongdong get respectively? Please fill in all possibilities in the table below:

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Analysis:10 =1+9 = 2+8 = 3+7 = 4+6 = 5+5 = 6+4 = 7+3 = 8+2 = 9+1.

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7.？ Two pirates are divided into 20 gold coins. Excuse me:

(1) If each pirate gets at least five gold coins, how many different ways can a * * * be divided?

(2) If each pirate can get at most 16 gold coins, how many different ways can a * * * be divided?

Analysis: (1) 1 1 species; (2) 13 species

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8.？ There are 15 glasses. How many different ways are there to divide them into two piles? How many balls may there be between these two piles?

Analysis: 7 kinds; There may be differences between 13, 1 1, 9, 7, 5, 3, 1.

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9.？ Grandma Zhang went to the supermarket to buy 12 boxes of bright milk, and found that these milk need to be put in two identical bags, and each bag can only hold 10 boxes at most. How many different ways does Grandma Zhang dress?

Analysis: 5 kinds

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10.？ Xiaoyue, Dongdong and Archie have seven extracurricular books, and everyone has at least one. How many extracurricular books are there in Xiaoyue, Dongdong and Archie? Please write down all possible situations.

Analysis: As shown in the following table, * * * has 15 possibilities.

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Extended article

1.？ As the picture shows, Xiaoyue painted a small house. If she can't transfer every stroke, how many strokes has she drawn at least?

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Analysis: 3 1 transaction

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2.？ Xiaoyue arranges 8 pieces of mung bean cakes as shown in the figure, and asks Dong Dong to choose two pieces of mung bean cakes that are close together. Excuse me: How many different ways are there to choose "Dong Dong Yi"?

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Analysis: 7 kinds

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3.？ Xiaoyue, Dongdong and Archie went to the movies. They bought three tickets for adjacent seats. How many different seating arrangements are there for the three of them?

Analysis: 6 kinds

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4.？ Xiao Li set up a stall to sell goods, each puppet sold 1 yuan, and each big puppet sold 2 yuan. He sold five puppets today. How much may Xiao Li sell today?

Analysis: 5 yuan, 6 yuan, 7 yuan, 8 yuan, 9 yuan or 10 yuan.

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5.？ The teacher gave Xiaoyue 14 identical exercise books. If Xiaoyue gives all these books to Dongdong and Archie, how many different ways are there?

The teacher gave Xiaoyue 14 an identical exercise book. If Xiaoyue only needs to divide these books into two piles, how many different ways are there?

Analysis: (1) 15 species (2)7 species.

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6.？ There are 20 peanuts on the plate. Abortion and Dongdong eat together. Everyone eats two peanuts in one bite, and two people eat peanuts together (at least one bite each). How many peanuts may they have eaten separately?

Analysis: 20 = 2+18 = 4+16 = 6+14 = 8+12 =10 =10.

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7.？ As shown in the figure, there are seven buttons with seven numbers written on them: 1, 2, 3, 4, 5, 6, 7. Excuse me:

(1) Select two keys so that the difference between the numbers on them is equal to 2. How many ways can I choose a * * *?

(2) Select two keys so that the sum of the numbers on them is greater than 9. A * * *, how many choices are there?

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Analysis: (1)5 species (2)6 species.

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8.？ Xiao Wang has five identical airplane models, and he wants to put them on a three-story shelf, with at least 1 on each floor. How many different versions does Xiao Wang have? In a few days, he will put the same car model 18 on another three-story shelf, with at least five cars on each floor. How many different ways are there?

Analysis: 6 kinds; 10 species

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9.？ (1) Xiaoming bought a bag of candied beans. He counted, 10. Now he is going to divide these jelly beans into three piles. How many different ways are there to divide a * * *?

(2) If Xiao Ming has two bags of jelly beans, each bag contains 10. These two bags of jelly beans should be divided into three piles, each pile should have at least five. How many different ways are there?

Analysis: (1)8 species; (2) Five kinds

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10.？ A, B, C, D and E answered a question together, and only two of them got it right. How many possible answers are there?

Analysis: 10 species

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1 1.？ (1) has two identical white balls and 1 red balls. If these three balls are arranged in a row, how many different arrangements are there?

(2) There are two identical white balls and three identical red balls. How many different arrangements are there for these five balls?

Analysis: (1)3 species (2) 10 species.

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12.？ The head teacher wants to choose four children from five children A, B, C, D and E to take part in the table tennis competition. How many different ways are there? If you have chosen A, B, C and D, how many different ways are there to divide into two groups to play doubles?

Analysis: 5 kinds; three kinds

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Beyond the article

1.？ Xiao Ming took part in a quiz, with 2 points for each small question and 5 points for each big question. There are three questions in each of the two types of questions. How many different possibilities are there for Xiao Ming to type a * * *?

Analysis: 16 species

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2.？ Some children are playing with stones, scissors and cloth in the house. Dongdong asked them how many people there were at the door. One of the children said, "I can't tell you the figures directly, but now we have 22 fingers sticking out and three people are throwing stones." Excuse me: How many people may be playing games in the room? Those who produce stones don't stretch their fingers, those who produce scissors stretch 2, and those who produce cloth stretch 5.

Analysis: 8 people, 1 1 person or 14 people.

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3.？ There are four questions in the test. At the beginning, each student's basic score was 4. Then add 3 points for each correct answer, and deduct 1 point for each wrong answer. What's the student's score?

Analysis: The score may be: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, with/kloc.

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4.？ Now there are five coins with 1, 2, and 5 cents. How many different ways are there to make 20 cent coins with these coins?

Analysis: 8 kinds

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5.？ As shown in the figure, Mom wrote five numbers 1, 1, 1, 2, 2 on five cards, and asked Xiao Ming to choose three cards from them to form a three-digit number. How many different three digits can Xiao Ming form?

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Analysis: 7

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6.？ Teacher Liu will go to the gym three times a week, but in order to prevent excessive exercise, he can't go for two consecutive days. How many kinds of schedules does Mr. Liu have that meet the requirements?

Analysis: 10 species

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7.？ On the abacus, how many different four digits can two beads represent?

Analysis: 14

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8.？ On the elevator of the 99-story skyscraper, there is an LCD screen showing the floor. As shown in the figure, due to screen damage, 1 of the seven line segments displaying the left number cannot be lit, and three of the seven line segments displaying the right number cannot be lit. Excuse me, how many floors are displayed correctly when the elevator is running?

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Analysis: 12

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