Depth analysis of permutation and combination differences: revealing differences

1, the difference between arrangement and combination Arrangement and combination are common concepts in combinatorial mathematics, which are used to describe different arrangements or combinations of objects. Although there is a clear definition in mathematics, people often confuse these two concepts in daily life.

2. What is arrangement refers to the way of arranging a group of objects in a certain order. In the arrangement, each object can only appear once in the arrangement, and the position of each object is fixed.

3. What is combination refers to the way of selecting several objects from a group of objects to form a subset, regardless of the order of the objects. In a combination, each object can only be selected once, and the position of the selected object is not important.

4. The difference between permutation and combination The main difference between permutation and combination lies in the consideration of the order and repeatability of objects. In the arrangement, the order of objects is very important, and each object can only appear once in the arrangement.

5. The application of the concept of example arrangement and combination has been widely used in many fields.

6. Conclusion permutation and combination is an important concept in combinatorial mathematics, which is used to describe different permutations or combinations of objects.

Arrangement:

Please ask three of the seven students to line up. How many different arrangements are there?

Why is this happening? As we can imagine, there are three positions to be filled in three steps:

There are seven situations when the first position is filled by someone.

Find someone to fill the second position. Judging from the remaining six people, there are six situations.

Find someone to fill the third position. Judging from the remaining five people, there are five situations.

According to the principle of multiplication, multiplication is used step by step, which is 7x6x5.

Combination:

Ask three of the seven students to form a group. How many different combinations are there? Why on earth do you calculate like this?

Because there were different arrangements within the three people at the time of arrangement, now they are uneasy to arrange, just need to merge into one group. So to get rid of the order in the group, divide it by the full arrangement of 3, and factorial 3 will do.