One 、 meaning
Permutation and combination , It is mainly used to calculate the number of methods or cases . Briefly , It's counting . It's different from the way we calculated it before , No longer in the form of enumeration , It's counting by permutation , The purpose is to prevent double counting or omission .
Two 、 Step by step
( One ) classification
Judgment method ： Each class can complete the task independently .
Calculation principle ： The principle of addition , Get one thing done , It needs to be divided into several categories , There are different ways to do this on your own . When this classification is not repeated 、 When there is no omission , The total number of methods to do this is equal to the sum of the number of methods of each class .
Example 1： Wang is on a business trip from place a to place B , If every day from place a to place B there are 4 A flight 、6 Train 、3 A long-distance bus , Ask Wang how many different ways there are from place a to place B ?
A. 3 B. 13 C.22 D.27
analysis ： The question goes from a to B , All in all 3 In this case , They are flights 、 Trains and coaches . Each way can complete the task independently ( From a to B ), So this question should be classified , The total number of methods is 4+6+3=13, So the choice of this question is B.
( Two ) Step by step
Judgment method ： Each step can't be completed independently .
Calculation principle ： Multiplication principle , Get one thing done , It needs to be divided into several steps , The method in each step just completes that step , After all the steps, just finish this thing , Then the total number of methods to complete the task is equal to the product of the number of methods in each step .
Example 2： Two of the three workers from a, B and C are on duty on Saturdays and Sundays respectively , How many different choices are there ?
A.3 B.6 C.9 D.12
analysis ： The problem starts from a, B and C 3 People choose 2 People on duty , Alone on Saturday ( Or Sunday ) Can not complete the task of this problem ( Choose the person on duty on Saturday and Sunday ), So this problem should be solved step by step , Let's make sure that the number of methods for Saturday is 3, The number of ways to determine the Sunday is 2, So the total number of methods is 3*2=6, So the choice of this question is B.
By comparing the above 2 questions , The difference between classification and distribution is whether the task can be completed independently .
3、 ... and 、 Permutation and combination
array , From n Any of the different elements m They are arranged in a certain order , The number of permutations is recorded as A(m,n), If it's directly to n There are three different elements arranged , Namely A(n,n), be called “ Full Permutation ”.
Combine , From n Take out... Of the different elements m As a group of , The number of combinations is recorded as C(m,n). Unlike the permutation , The combination focuses only on what is taken out , Regardless of the order of removal .?
difference ： From the selected elements , Take any two , Exchange order , If the results are different , It's arrangement , Otherwise it's a combination .
Example 3： A department from 8 Out of a staff of 4 People attend training , among 2 People attend computer training ,1 Many people take part in English training ,1 People attend financial training , How many different choices are there ?
A.256 B.840 C.1680 D.5040
analysis ： According to the title , The question is how to choose , There is no order between elements . First of all, from the 8 Of the elements 2 People attend computer training , The number of methods is C(2,8)=28, And from the rest 6 People choose 1 Many people take part in English training , The number of methods is C(1,6)=6 Kind of , Finally, from the rest 5 People choose 1 People attend financial training , The number of methods is C(1,5)=5 Kind of , So the method number 28*6*5=840, choice B.
The basic knowledge of permutation and combination is the key to solve the later related problems , meanwhile , It's also the basis of probability , So we must master the basic knowledge in place , Not greedy , Only for perfection !
That's the quantitative relationship , Part of the test preparation content of the problem-solving skills of quantitative relationship in line test , Professional ability test column also provides quantitative relationship for you 、 Judgment and reasoning, etc .