Generally speaking, taking out m(m≤n) elements from n different elements and arranging them in a certain order is called the arrangement of taking out m elements from n elements. According to the definition of permutation, two permutations are the same if and only if the elements of the two permutations are exactly the same and the arrangement order of the elements is also the same. For example, the elements of abc and abd are not exactly the same, but are in different arrangements; Another example is abc and acb. Although the elements are exactly the same, the arrangement order of the elements is different, which is also a different arrangement.

Definition of combination:

From m different elements, taking out n elements at a time, no matter what order, is called combination.

The difference between the two is that the arrangement is related to the order of elements, and the combination has nothing to do with the order. For example, 23 1 and 2 13 are two permutations, and the sum of 2+3+ 1 is a combination.

Now answer your question:

The above ideas to solve the problem are correct.

However, if the following questions also use the above method 1 (that is, the arrangement method), the process is very complicated, and all possible arrangement orders need to be listed before the probability can be obtained. (Specifically: red, white, black, red, black, white, black, red, white, black, white, red, black, red, white).

A, three of 15 are arranged first, so a =15 *14 *13 = 2730.

B, to take a white ball, a black ball and a red ball, you need to take one from each of the six white balls, five black balls and four red balls, with 6*5*4= 120, and then arrange the balls in different ways according to B= 120*6=720.

C, so the probability is: B:A=24/9 1.

Obviously, it is very convenient to use the combination method here. Because the color order of each ball is not considered, the combination solution is directly used:

A, first choose 3 from 15, then b = (15 *14 *13)/(3 * 2 *1) = 455.

B, because one of the white, black and red balls is required, C=6*5*4= 120.

C, the answer is C:B=24/9 1.

There is a better way, that is, to use the distribution function method in college probability statistics and directly use the hypergeometric distribution formula to solve it. I won't introduce it here.

I hope I can help you!