The meaning of A used in calculating probability, how to calculate it, and the difference between C

a represents the arrangement, a superscript m subscript n means that m of n numbers is drawn out of n numbers and then arranged = n(n-1)(n-2).n-m+1)=n!/(n-m)!

c represents the combination, c superscript m subscript n represents the number of methods to extract m numbers out of n numbers =n!/[m!(n-m)!]

1. The calculation formula of c:

c represents the number of combination methods, for example: c(3,2), which means that 2 of the 3 objects are selected, and the total method is 3, which are AB, A, C, and B C (when the 3 objects are not the same).

2. The formula for calculating a:

A represents the number of arrangement methods, for example: n different objects, to take out m (m<=n) to arrange, the method is a(n, m) kinds, you can also think of it this way, the first one has n choices, the second one has n-1 choices, and the third has n-2 choices... The m has n+1-m options, so the total permutation is n(n-1)(n-2)·· n+1-m), which is also equal to a(n,m).

Two commonly used permutations: basic counting principles and applications:

1. Addition principle and categorical counting method:

Each method in each category can accomplish this task independently, and the specific methods in the two different types of methods are different from each other (i.e., the classification is not duplicated), and any method to complete this task belongs to a certain category (i.e., the classification is not omitted).

2. Principle of multiplication and step-by-step counting method of bright accompanying beam:

One method of any step cannot complete this task, and Jingyun only needs to complete these n steps in a row to complete this task, each step count is independent of each other, as long as the method taken in one step is different, the corresponding method to complete this matter is also different.

c denotes the number of combinatorial methods, and a denotes the number of permutation methods. If there is no order for the individuals selected in this question, use the combination, and if there is a order, use the arrangement.

Probability theory c and a calculation formulas.

1. The calculation formula of c:

c denotes the number of combined methods.

For example, c(3,2) means that 2 of the 3 objects are selected, and the total method is 3, which are AB, AC, and B C (when the 3 objects are not the same).

2. The formula for calculating a:

a denotes the number of permutation methods.

For example, cavity failure: n objects with different Wu Zhi tremors, to take out m (m<=n) for arrangement, the method is a(n,m) species.

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, ·· The m has n+1-m options, so the total permutation is n(n-1)(n-2)·· n+1-m), which is also equal to a(n,m).

Note: In the specific topic, it depends on whether the question needs to be arranged or combined, that is, whether the monomer needs to be ordered, use A if you need it, and use C if you don't need it.

3 Probability Theory. Bayes' theorem, probability theory, or probability theory, is the mathematics that studies phenomena such as randomness or uncertainty. More precisely, the theory of probability is used to simulate the situation in which an experiment will produce different results in the same environment.

Typical random experiments include dice rolling, coin toss, poker probability theory, and roulette games.

First, the nature is different.

1. "A": A stands for arrangement, take out m (m n) elements from n different elements and arrange them in a column in a certain order, which is called an arrangement of m elements from n elements.

2. "C": C stands for combination, which means that there are several ways to combine several numbers, regardless of the order of the numbers.

Second, the definitions are different.

1. "A": arrangement, one of the important concepts of mathematics. The subsets of a finite set are arranged in columns, in a circle, not allowed to be repeated or repeated, etc., according to the sequencing method of certain conditions.

Removing m (1 m n) different elements from n different elements at a time and arranging them into a column is called an unrepeating arrangement or straight arrangement of m elements from n elements, referred to as arrangement.

2. "C": Combinatorial, one of the important concepts in mathematics. Taking out m different elements (0 m n) from n different elements at a time, regardless of their order, is called selecting a combination of m elements from n elements without repeating.

Third, the rules are different.

1. "A": Repeated arrangement is a special arrangement. Repeat the selection of m elements from n different elements.

Arranged in a certain order, it is called a repeatable arrangement of m elements from n elements. Both permutations are the same if and only if the elements taken are the same and the order in which the elements are arranged is also the same.

It is easy to know from the principle of step-by-step notation, and the number of different permutations of m elements is taken from n elements.

2. "C": CombinationwithRepetiton is a special combination. Repeat the selection of m elements from n different elements.

Regardless of its sequential composition, it is called a repeatable combination of m elements taken from n elements.

If and only if the same element is taken, and the same element is taken the same number of times, then the two repeats are combined. The number of different combinations of m elements that can be reproducibly selected from n different elements is denoted as.

or, and.

The formula for calculating the probabilities c and a is as follows: the permutation is represented by a, a (right superscript m, subscript n) = n!/（n-m）!

The combination is represented by c, c (right superscript m, subscript n) = n!/[m!（n-m）!

Punch C represents the number of combination methods, and A represents the number of bending and bending methods. If the individuals selected in the question do not have a precedence, use a combination, and if there is a precedence, use a permutation.

28: Class A and Class C, what's the difference?

The formula for calculating a and c in probability is a: p(a) = conditional probability total probability p(a) = p(a|).b)/p(b)。c: p(c) = conditional probability total probability p(c) = p(a|c)/p(c)。

In probability, c is a combination, a is a permutation, if the individuals selected in the problem do not have a precedence, use a combination, if there is a precedence, use permutation.

The use of c and a in probability each:

c denotes the number of combined methods. For example, c(3,2) means that 2 of the 3 objects are selected, and the total method is 3, which are AB, A, C, and B. (3 objects are not the same case).

a denotes the number of permutation methods. For example, n different objects, to take out m (m<=n) for arrangement, the method draft imitation is a(n, m) kind. It can also be like this, the first one has n choices, the second has n-1 choices, the third has n-2 choices, ·· The m has n+1-m options, so the total permutation is big bi n(n-1)(n-2)·· n+1-m), which is also equal to a(n,m).