For example, c (3,2) means to select two objects from three objects, total * * *, and there are three methods, namely, A, B and C (three objects are different at the same time).

A indicates the number of arrangement methods.

For example: n different objects, to take out m (m

You can also think of it this way: the first one has n choices, the second one has n- 1 choices, the third one has n-2 choices, and the m-th one has n+ 1-m choices, so the total * * arrangement method is n (n-65438+).

Extended data:

Classical definition

If the test meets two requirements:

(1) The experiment has only a limited number of basic results;

(2) The possibility of each basic result of the test is the same.

Such an experiment is a classic experiment.

For event A in the classical experiment, its probability is defined as: P(A)= 1

Where n represents the total number of all possible basic results in the test. M represents the number of basic test results contained in event A. This method of defining probability is called the classical definition of probability.

Frequency definition

As the problems people encounter become more and more complicated, the equal possibility gradually exposes its weakness, especially for the same event, different probabilities can be calculated from different equal possibility angles, resulting in various paradoxes.

On the other hand, with the accumulation of experience, people gradually realize that when doing a large number of repeated experiments, with the increase of the number of experiments, the frequency of an event always swings around a fixed number, showing certain stability. R.von mises defines this number as the probability of an event, which is the frequency definition of probability. Theoretically, the frequency definition of probability is not rigorous enough.

Statistical definition

Under certain conditions, the experiment was repeated n times, where nA is the number of times that Event A occurred in n times. If with the gradual increase of n, the frequency nA/n gradually stabilizes around a certain value p, then the value p is called the probability of the occurrence of event A under this condition, and it is recorded as P (a) = P .. This definition is called the statistical definition of probability.

In history, Jacob Bernoulli is the first person to give a strict meaning and mathematical proof to the assertion that "when the number of experiments n increases gradually, the frequency nA is stable at its probability p".

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