Definition of arrangement: from n different elements, any m(m≤n, m and n are natural numbers, the same below) elements are arranged in a column in a certain order, which is called the arrangement of taking out m elements from n different elements; All permutation numbers of m(m≤n) elements taken from n different elements are called permutation numbers of m elements taken from n different elements, which are represented by symbol A(n, m).
Definition of combination: taking any m(m≤n) elements from n different elements to form a group is called taking the 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. Represented by the symbol C(n, m).
Extended data:
Basic counting principle of permutation and combination
A, addition principle and classified counting method.
1. addition principle: There are n ways to accomplish one thing. In the first way, there are m 1 different ways, in the second way, there are m2 different ways ... in the n ways, there are mn different ways, so there is n = M 1+M2+M3+...+Mn to realize it.
3. The method of the first method belongs to the set A 1, and the method of the second method belongs to the set A2 ........................................................................................................................................
3. Classification requirements: each method in each category can accomplish this task independently; The specific methods in the two different methods are different from each other (that is, the classification is not heavy); Any method to accomplish this task belongs to a certain category (that is, classification does not leak).
Second, the multiplication principle and step-by-step counting method
⒈? Multiplication principle: to do one thing, it needs to be divided into n steps. There are m 1 different methods to do the first step, m2 different methods to do the second step ... There are mn different methods in step n, so there are N=m 1×m2×m3×…×mn different methods.
4. Reasonable step-by-step requirements: this task cannot be completed in one way at any step, and this task can only be completed by continuously completing these N steps; Each step is independent of each other; As long as the methods used in a step are different, the corresponding methods to complete it are also different.
3. It is also closely related to the later discrete random variables.
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