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How many of the five numbers are multiples of 4? (permutation and combination) Please explain how to do it
If the last two digits are 20, 24, 40, 64, 04 and 60, it is a multiple of 4. When the last two digits are 20, 24, 40, 64, 04 and 60, the first three digits have 3 * 2 * 1 = 6 permutations, and 6 * 4 = 24. When the last two digits are 64 and 24, the first three digits have 2 * 2 * 1 = 4, 4 * 2 = 8 + 24 = 32 permutations
Take any three of the five numbers 2, 3, 4, 7 and 9 to form a three digit number without repetition. There are three problems
1. How many such three digits are there?
2. What is the sum of all the three digit numbers?
3. What is the sum of all these three digits?
(1) So it's 10X6 = 60 (2) because the chance of each number is equal. So they appear 12 times in each digit. So, (2 + 3 + 4 + 7 + 9) X12 = 300 (3) because when we add all the three digits, we know that no matter how the position of the single digit changes
Permutation and combination problem: use 1, 2, 3, 4, 5, 6, 7, 8 and 9 to form a non repetitive nine digit number, but 1 should be in front of 2
, find the number of nine digits that meet the requirements,
Method 1
9!/2=181440
All of them are arranged as 9! In which the number of 1 before 2 and 2 before 1 are equal, so they each account for one and a half
Method 2
Choose two of the nine positions to put 1 and 2 first, and the method is C (9,2) = 9 * 8 / 2
The remaining 7 numbers are arranged randomly. The method is 7!
The qualified order is 9 * 8 / 2 * 7! = 9! / 2 = 181440
RELATED INFORMATIONS
- 1. The six numbers from 0 to 5 make up four digits, which can be divided by 25. How many such numbers are there without repetition
- 2. The permutation and combination are composed of numbers 1.2.3.4.5. How many of the three digits without repetition can be divided by 9
- 3. Permutation problem, master please! Online 0-9 combined into 5 digits, how many? Thank you~~~~~ 0123456789 these ten numbers, combined into five digits, there are repeated count 1, such as 12345 or 54321 or 25314, etc., such as the same count 1, that is to say, do not count according to the arrangement. If such conditions, how many combinations in total? Thank you! Drbtly, how do you calculate your 10080? 252 of desert island 840611 is definitely wrong I'm 2000 myself. Can I give you more answers? Back to 517290352: at the beginning of the question, my condition is that "12345 or 54321 or 25314 and so on are all equal to one, that is to say, they do not need to be calculated according to the arrangement". Although 12345 and 54321 are two five digit numbers, are they all composed of 12345, regardless of the order of arrangement, they can be regarded as one, All count as one~~
- 4. Use a total of 6 numbers from 0 to 5 to form 6 digits larger than 240135. How many are there? I hope to give a detailed answer (using permutation and combination)
- 5. 123456 is written on the six faces of a cube to determine the number of faces of each number
- 6. A small cube block is marked with six numbers 1, 2, 3, 4, 5 and 6 on its six faces. How many different situations can we see at most on one or several faces of the cube from different angles?
- 7. The number of six digits is () A. 40B. 60C. 80D. 10
- 8. How many quadruple digits can 123456 make up
- 9. How many 4-digit numbers can be formed by 123456 without repetition and divisible by 3?
- 10. Use 123456 to form a six digit ABCDEF without repetition, so that ABC, BCD, CDE and def are multiples of 4, 5, 6 and 11, respectively
- 11. In the number 1-33, randomly choose 6 digits so that the sum of 6 is 100. How many choices are there? What is the formula? Is this a permutation?
- 12. Two similar permutation and combination questions, in 1.2.3.4 these four numbers constitute three digits without repeating numbers, in which the odd number has 2. Take any three digits from the six numbers 0-5 to make up the unrepeated number, of which the even number is Please let me know by permutation,
- 13. Natural numbers 1, 2, 3 In the order of 123456 910112… If it reaches 2889 digits, the sum of all digits
- 14. The permutation and combination of four numbers 1234 is composed of: one two three four twelve thirteen fourteen twenty-three twenty-four thirty-four one hundred and twenty-three . How many combinations are there? And how are they calculated? There is no requirement for the order of arrangement
- 15. Take any 4 digits from 0 to 9 to form a 5-digit permutation The number permutation and combination problem of 0-9 Any four of the ten digits from 0 to 9 make up five digits. 0 can be placed in the first place. The first three digits must not be the same, and the last two digits can repeat at most one digit with the first three digits. How many digits are there, Any four of the ten digits 0-9 make up five digits. 0 can be put in the first place. The first three digits can't be the same. The last two digits can repeat only one digit and the last two digits can be the same. How many permutations are there
- 16. What's the total number of 0-9 permutations in a group of four, the most complete answer, thank you!
- 17. When a () is multiplied by a, the product is greater than 5 / 9; when a () is multiplied by a, the product is less than 5 / 9 In addition, the side length of a square is one fourth of a meter, its perimeter is () meters, and its area is () square meters. Why?
- 18. 1/21+5/8+4/9+3/7=
- 19. (- 1 / 63) / (1 / 9-2 / 7 + 2 / 3-4 / 21)=
- 20. 987 × 655-321 of 666 + 987x654 is calculated