First of all, this classmate, according to your answer, you don't have a good command of "arrangement/combination" of mathematical tools (you don't know anything about C, okay ...). This is what you need to learn in senior two mathematics, but you don't need any foundation. Let me say it briefly.

Of course, I will answer your question, but you should know what combination is.

Baidu Encyclopedia says that taking out n elements from m different elements at a time, no matter what order, is called combination. Here is "in any order", which means I choose 5 out of 20 numbers. Suppose they are 1, 2, 3, 4, 5, then even if I take 1 3 2 4 5 or 5 3 1 2 4 in sequence, it is the same. The expression of four words is: no order.

Then clear your mind: that is, draw five numbers from 1~20, out of order!

Then randomly select a group of numbers, such as a b c d e, and gradually extract: if you extract the first number A from 20 numbers, then you have 20 choices in the first extraction; After drawing A, you still have 19, so if you want to draw the second number, you have the choice of 19; Similarly, with the number 345 left, you will face the choice of 18 17 16. So how many choices do you always have?

You can draw a tree diagram. After the first number is selected, there will be 19 kinds after each choice. After the second choice, there will be 18 kinds after each choice ... then you will understand that it is multiplication! There are 20 * * *19 *18 *17 *16 kinds!

Then I'll tell you it's wrong. As I said before, this is not continuous. Your drawing method is "sequence". Why? When we discuss one by one critically, we are actually discussing the order. Because we are "the first", "the second" and "the third", the tree diagram is drawn from top to bottom (in short, from one side to the other), which actually means order. Then we need to "exclude" and "repeat" all the choices.

Going back to the two "repeated" choices mentioned in the second paragraph: 1 3 2 4 5 and 5 3 1 2 4, which are actually like ABC D E, if you want to change the order of these five numbers, then we will take the same thinking as discussing the problem (thinking about the order, how not to talk about the order, the thinking is written in detail above, please refer to it), and we can draw a conclusion, no matter what. So the combination we need is 20 *19 *18 *17 *16 (5 * 4 * 3

If you don't understand anything, just ask me. I will answer as soon as possible after logging in all the year round.