Arrangement and combination and Basic counting principles

Arrange

From n different elements, any M elements are arranged into a column in a certain order (m ≤ n, m and n are all natural numbers, the same below ), it is called an arrangement for retrieving M elements from n different elements.

The number (m ≤ n) of all the M elements from n different elements is called the number of M elements from n different elements, it is represented by the symbol A (n, m.

A (n, m) = N (n-1) (n-2 )...... (N-m + 1) = n! /(N-m )!

In additionRule 0! = 1 (n! Represents N (n-1) (n-2)... 1,That is, 6! = 6x5x4x3x2x1

 

Combination

From n different elements, any M elements are combined into a group (M ≤ n), which is called a combination of M elements from n different elements.

The number of all combinations of M (m ≤ n) elements from n different elements is called the number of combinations of M elements from n different elements, it is represented by the symbol C (n, m.

C (n, m) = a (n, m)/m!

C (n, m) = C (N, N-m), (n ≥ m)

 

Addition principle and classification COUNTING METHOD

Principle of addition: to do one thing, there can be n methods to complete it. There are M1 methods in the first method, and M2 methods in the second method, ......, There are Mn different methods in the N method, so there are n = m1 + M2 + m3 +... + Mn methods.

The method of the first method belongs to the set A1, and the method of the second method belongs to the set A2 ,......, Method N belongs to the set an, so the method used to complete this task belongs to the set a1ua2u... UAN.

Classification requirements: each method in each category can complete this task independently. The specific methods in the two categories are different (that is, the classification is not heavy ); any method used to complete this task belongs to a certain category (that is, the classification is not omitted ).

 

Multiplication principle and step-by-step counting

Multiplication principle: to do one thing, you need to divide it into n steps. In the first step, there are M1 different methods, and in the second step there are M2 different methods ,......, There are different Mn methods for Step N, so there are n = m1 × m2 × m3 ×... * Mn methods.

Reasonable and step-by-step requirements for Workers: A method in any step cannot complete this task. This task can only be completed after consecutive n steps are completed. The counts of each step are independent of each other; as long as the methods used in one step are different, the corresponding methods for completing the matter are also different.

 

Source

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Arrangement and combination

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