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When to use combination formula and when to use permutation formula? Don't give me from Baidu Encyclopedia to get that entry to me, I want to tell me specifically, an example, I understand
This needs to be analyzed in detail, but generally there is a principle, just like their names, "combination" means grouping, without considering position relationship; while "arrangement" should consider not only grouping, but also location. For example, if nine people are divided into three groups, then combination is used; while for nine people standing in three rows, arrangement is used, because position relationship must be considered when standing in a row
How much time difference is there between India local time and Beijing time? For example: India local time is 14:00 p.m., Beijing time is what time, how much difference?
e. G. 14:00 PM India time, 16:30 PM Beijing time
That's right. It's exactly two and a half o'clock, so it's about 10 o'clock in the evening. It's already midnight in China
For example, the actual distance of longitude and latitude, the time of time difference What's the skill? What's the formula It's better to have examples
Because the latitude lines are parallel lines, the distance between them is equal, and the difference is about 111 kilometers. For example, from the equator to 10 degrees north latitude, the distance is about 1110 kilometers
How to calculate the time difference of geographical time zone is OK. It's better to illustrate it with examples
Calculated time zone = known zone time - (time zone of known zone time - time zone of zone time to be calculated), (Note: the eastern zone is positive and the western zone is negative)
Example 1: it is known that Tokyo (East 9) time is 13:00 on May 1. What is the district time of Beijing (East 8 District)?
Beijing time = 13:00 - (9-8) = 12:00 (Beijing time is 12:00 on May 1)
Example 2: it is known that Beijing time is 12:00 on May 1. What is the district time of London (central time zone)?
London time = 12:00 - (8-0) = 4:00 (London time is 4:00 on May 1)
Example 3: it is known that Beijing time is 12:00 on May 1. What is the district time of New York (West five District)?
New York time = 12:00 - [8 - (- 5)] = - 1:00 + 24:00-1 day = 23:00 (i.e. New York time is 23:00 on April 30). (Note: when the calculated area time is negative, 24:00 should be added, and the date minus one day, that is, from May 1 to April 30)
Example 4: it is known that the New York time is 12:00 on May 1?
Tokyo time = 12:00 - [(- 5) - 9] = 26:00-24:00 + 1 day = 2:00), that is, Tokyo time is 2:00 on May 2. (Note: when the calculated area time is greater than or equal to 24:00, 24:00 should be subtracted, and the date plus one day is changed from May 1 to May 2)
Judging the old and new days depends on two lines
One is the artificial date line of 180 degrees
The second is the natural dividing line, which is the meridional line at 0:00 local time
The date passing 0 o'clock is added one day from west to East
One day from west to East after 180 degrees
How much is the difference between New York time and Beijing time? How to calculate the time difference? It's a little confusing. I hope you can give me a simple method
The time difference between Beijing and New York is 13 hours
(daylight saving time is implemented from the first Sunday in April to the last Sunday in October, which is 12 hours short
New York time = Beijing time minus 13 hours (daylight saving time minus 12 hours)
For example, it is 10:20 on July 29, 2013, and 22:20 on July 28, 2013 in New York
The following table lists the time difference between several foreign cities and Beijing ("- 1" means that the time is one hour earlier than Beijing time). The current Beijing time is 8:00 a.m (1) What's the time in Tokyo now? (2) Bin Bin wants to call his aunt in Paris now. Do you think it's appropriate? City time difference / hour New York - 13 Paris-7 Tokyo + 1 Chicago - 14
(1) 8 + 1 = 9,
Now Tokyo time is 9 a.m;
（2）8-7=1，
The time in Paris is 1 o'clock in the morning, and my aunt is sleeping
After rearranging the four digit numbers, some new four digit numbers can be obtained. The existing four digit m is 7956 smaller than the largest one in the new number and 396 larger than the smallest one in the new number. Find the four digit number and briefly explain the reason. (the four digits of M can be the same, but excluding the digit 0)
If the largest four digits of the composition are x, then x = m + 7956; if the minimum four digits of the composition are y, then y = m-396x-y = 7956 + 396 = 8352, and the highest order of difference is 8, then the highest digit of X is 9, and the highest order of Y is 1
How does permutation formula deduce combination formula? Please give detailed explanation, thank you! It's better to explain the proof process of permutation formula!
The permutation formula is to establish a model, take M elements from n different elements and arrange them into a column (in order). The first position can have n choices, the second position can have n-1 choices (one has been placed in the previous position), then the third position can have n-2 choices, and so on, the M position can have N-M + 1 choice, then the permutation number a (n m) = n * (n-1) * (n-2)... * (n-m + 1)
According to the definition of factorial, a (n m) = [n * (n-1) * (n-2)... * (n-m + 1)] * [(n-m) * (n-m-1)... * 1] / [(n-m) * (n-m-1)... * 1]
A (n, m) = n! / (n-m)!
The combination formula corresponds to another model. Taking m elements into a group (disorder), we can consider permutation a (n, m). Because a group of M elements can have m! Different permutations (Full Permutation a (m m) = m!), the total number of combinations is a (n m) / m!
That is, C (n m) = a (n m) / m! = n! / [M! * (n-m)!]
Any three of the six numbers 1, 2, 3, 4, 5, 6 can be selected to form a three digit number. What are the combination methods? The formula is required
C(6,3)=6*5*4/(3*2)=20!
1 2 3
1 2 4
1 2 5
1 2 6
One hundred and thirty-four
One hundred and thirty-five
One hundred and thirty-six
One hundred and forty-five
One hundred and forty-six
One hundred and fifty-six
Two hundred and thirty-four
Two hundred and thirty-five
Two hundred and thirty-six
Two hundred and forty-five
Two hundred and forty-six
Two hundred and fifty-six
Three hundred and forty-five
Three hundred and forty-six
Three hundred and fifty-six
Four hundred and fifty-six
There are 20 kinds of combinations! Each of them can form 3! = 6 different three digit numbers, so there are 20 * 6 = 120 numbers
In fact, P (6,3) = 6 * 5 * 4 = 120!
How many different three digits can 12345 make up
If the numbers can be repeated, there are: 5 × 5 × 5 = 125
If the numbers can not be repeated, there are: 5 × 4 × 3 = 60
RELATED INFORMATIONS
- 1. How many five digits can you make up with 12345?
- 2. There are 120 five digits made up of 1, 2, 3, 4 and 5. Put these five digits in order from small to large, and the 95th number is______ .
- 3. The number of a column: 1,3 + 5,7 + 9 + 11,13 + 15 + 19,12 + 23 + 25 + 27 + 29?
- 4. The number of columns arranged according to the regulations is 2, 3, 10, 15, 26 and 35. What is the seventh number? If the answer is right, a reward will be offered!
- 5. Look at the following list: half, one sixth, one twelfth, one twentieth Please find out the rule of arrangement and press here Fill in the blank regularly The fifth number is—— The number in 2011 is——
- 6. -3 / 4, 5 / 7, - 10 / 9, 17 / 13, - 33 / 16 to find the law, what is the number 2012
- 7. In extracurricular activities, four people report the number. A says: 1. B says 2, C says 3, and Ding says 4. In this way, the total number of people reported is more than money. Ask 34 who reported it. 71 who reported it
- 8. 55 students from class 5 (1) of a school formed a large circle. From the first student, the number was counted by 1, 2, 3 and 4. When the last student finished the report, the first student continued to report down according to the law. A total of 6 circles were reported. When the seventh circle began, the first student reported how many, there was a formula, and then, explain why, talk about analysis
- 9. There are 47 students in a row. 1 to 3 count off, and the last student reports how many students are there in this team? The students who report one step forward and stand in a line?
- 10. 1999 students in a row, from the front to the end of the line 1 to 3, and then from the end of the line to the front 1 to 4 1999 students in a row, from the front to the end of the line 1 to 3, and then from the end of the line to the front 1 to 4. How many of them reported 1 twice
- 11. How do these numbers find the rule 1, 2, 4, 8, 16, 32 Up to 64, how much does it add up to? What is the rule formula?
- 12. Observe the number of the following columns in order of + 2, - 4, + 6, - 8, + 10. According to its sorting rule, the number of 2012 should be?
- 13. The earliest mathematical masterpiece in the world is "nine chapters on arithmetic". What is the earliest "origin of species" in the world?
- 14. There is a mathematical Pythagorean theorem problem It is known that there are two fishing boats in port B. ship a and ship b set out at the same time. If ship a goes along the direction of 60 degrees north by east at a speed of 8 nautical miles per hour, ship B sails along the direction of 30 degrees south by East with a speed of 9 nautical miles per hour. Two hours later, ship a arrives at Island m and ship B sails to island P. please estimate the distance between island m and island P
- 15. Chinese mathematicians Who knows? Easy!
- 16. The definition of Pythagorean theorem, specific
- 17. The problem of calculating the area of double knobs by integral It seems that θ can't take pi / 4 to pi / 2? When drawing, is the graph in the first quadrant only 0 to pi / 4? So when integrating in polar coordinates, the upper limit of integration is pi / 4, right? And I still don't know whether the angle in polar coordinates is determined by the angle between the X axis and the X axis, and the graphs with angles not in the defined domain will not be drawn Although it seems that the graph is continuous, its value of θ is not continuous, is it? Thank you!
- 18. Find 20 Pythagorean theorem to solve more problems!
- 19. What do you mean by listening? Be simple and clear! Use it in primary school science
- 20. Find some English stories. Do me a favor. On Wednesday, I have to Hope is some fairy tales in English