Formula: C(n, m)=A(n, m)∧2/m! =A(n，m)/m！ ; ? C(n, m)=C(n, n-m). (where n≥m)
Combination introduction:
Combination is one of the important concepts in mathematics. Taking out m different elements from n different elements at a time, regardless of the order, is called choosing the combination of m elements from n elements without repetition. The number of species in all such combinations is called the combination number.
The essence of combination
1, complementarity
That is, the number of combinations of m elements from n different elements = the number of combinations of (n-m) elements from n different elements;
This property is easy to understand, such as c (9,2) = c (9,7), that is, the method of selecting two elements from nine elements is equal to the method of selecting seven elements from nine elements.
Provisions: c (n, 0) = 1 c (n, n) =1c (0,0) = 1.
2. Combinatorial identities
If m item is selected from n items, the following formula exists: c (n, m) = c (n, n-m) = c (n- 1, m- 1)+c (n- 1, m).
Extended data:
Introduction to arrangement:
There are two definitions of arrangement, but there is only one calculation method. Those who meet these two definitions are calculated in this way.
The premise of the definition is that m≤n, and both m and n are natural numbers.
(1) From N different elements, any M elements are arranged in a column in a certain order, which is called the arrangement of taking out M elements from N different elements.
(2) Taking out all the arrangements of M elements from N different elements is called taking out the arrangements of M elements from N different elements.
Use specific examples to understand the above definition: four colors are arranged according to different colors, and there are as many arrangements as there are, and if there are six colors, there are as many arrangements. How many arrangements are there for four of the six colors?
Solution: A (4 4,4) = 4x (4-1) x (4-2) x (4-3) x (4-4+1) = 4x1= 24.
A(6，6)=6x5x4x3x2x 1=720。
A(6，4)=6！ /(6-4)! =(6x5x4x3x2x 1)/2=360 .