Combination and Arrangement

Combination:

Definition: n elements are extracted from m different elements each time,In whatever orderIs called a combination. The numbers of different combinations are represented by the symbol C n (superscript) m (subscript), C n (superscript) m (subscript) = M (S-1 )... (M-n + 1) = M! /(N! (M-N )!). In addition, C 0 (superscript) m (subscript) = 1. C n (superscript) m (subscript) = c m-N (superscript) m (subscript );

 

 

Arrangement:

Generally, the M (M limit N) elements are extracted from n different elements.A certain order is arranged into a columnIt is called an arrangement (Arrangement) for extracting M elements from n elements ).

According to the definition of the arrangement, the two are arranged in the same order. If the two elements are exactly the same, the order of the elements is also the same. For example, the elements of ABC and Abd are not exactly the same, and they are arranged differently. For example, although ABC and ACB are identical, the order of elements is different, they are also different.

The number of all the permutation numbers of M (m) elements from n different elements is called the number of M elements from n different elements, it is represented by amn.

Number arrangement formula:

 

 

An arrangement of all n different elements is called a full arrangement of n different elements. This is in the number arrangement formula, M = N, that is:

Ann = N · (n-1) · (n-2) · 3 · 2 · 1

That is to say, the number of arrays retrieved from n different elements is equal to the product of a positive integer between 1 and N. The product of a positive integer to N, called the factorial of N, with n! .

Full Permutation Formula

Ann = N · (n-1) · (n-2) · 3 · 2 · 1 = n !, We set 0! = 1