1, "a": a stands for arrangement, and m(m≤n) elements are taken out of n different elements and arranged in a column according to a certain order, which is called the arrangement of taking m elements out of n elements. .

2. "C": C stands for combination. Regardless of the order of the numbers, there are several ways to combine several numbers.

Second, the definition is different.

1, "a": permutation, one of the important concepts in mathematics. The subsets of finite sets are arranged in columns and are circular, and they are not allowed to be repeated or repeated according to some conditional sorting method. Take out m( 1≤m≤n) different elements from n different elements at a time and arrange them in a row, which is called non-repetitive arrangement or linear arrangement of taking out m elements from n elements, which is called arrangement for short.

2. "C": Combination, one of the important concepts in mathematics. Taking out M different elements (0≤m≤n) from N different elements at a time and synthesizing a group regardless of their order is called selecting the combination of M elements from N elements without repetition.

Third, the law is different.

1, "a": repeated arrangement is a special arrangement. You can repeatedly select m elements from n different elements. Arranging in a column in a certain order is called a repeatable arrangement of m elements starting from n elements. If and only if the selected elements are the same and the arrangement order of the elements is the same, the two arrangements are the same.

According to the principle of step-by-step counting, it is easy to know that the different arrangement numbers of m elements and n elements are as follows

2. "C": The combination with repetiton is a special combination. You can repeatedly select m elements from n different elements. Synthesizing a group of m elements called n elements regardless of their order is a repeatable combination.

Two repeated combinations are the same if and only if the elements are the same and the same elements are taken the same times. The number of different combinations of M elements can be repeatedly selected from N different elements as follows.

or

, and

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