Simple six-digit passwords are: 123456, 123789, 0 12345, 567890, 234567, 345678, 456789 and so on. (There are too many detailed data to list one by one) Six-digit password composition: For example, suppose that the six-digit password is abcdef, in which A can choose any one of the ten numbers from 0 to 90, suppose to choose 0, suppose to choose 0, and suppose to choose 0, as above, C, D, E and F also choose from the ten numbers from 0 to 90. Because, in the six-digit password, each digit is randomly selected from 10 digits from 0 to 9, and finally a six-digit password is formed, so the six-digit password * * has10 */kloc-0 *. 1. Try to use a strong password in the form of "letters+numbers+special symbols"; 2. Set passwords for online banking, online payment, common mailboxes and chat accounts respectively, and prohibit "one password from being used everywhere"; 3. Manage passwords at different levels according to the importance of accounts, and change passwords for important accounts regularly; 4. Avoid using information related to identity privacy, such as birthday, name pinyin and mobile phone number, because hackers often test this information before cracking the password of a specific target.

There are 1000000 groups (one million groups) of 6-digit passwords from 0 to 9, which means 1000000 possibilities.

Think about doing the problem:

0~9 has ten numbers, and each position can be 0~9, so it is easy to know that there are ten possibilities (0~9) for each bit of a six-digit password. This is a permutation problem which can be solved by multiplication. So the possibility of each position is multiplied, and the result obtained by multiplying 6 10 is10 *10 *10 *10 =10 =/kloc-.

Taking any m(m≤n) elements from n different elements and arranging them in a certain order is called the arrangement of taking m elements from n different elements. When m=n, all permutations are called total permutations.

Formula: Total permutation number f(n)=n! (Definition 0! = 1)

Extended data

difficulty

(1) Abstracting several concrete mathematical models from different practical problems requires strong abstract thinking ability;

⑵ The restrictive conditions are sometimes obscure, which requires us to accurately understand the key words (especially logical related words and quantifiers) in the question;

⑶ The calculation method is simple and has little connection with the old knowledge, but it needs a lot of thinking when choosing the correct and reasonable calculation scheme;

(4) Whether the calculation scheme is correct can't be tested by intuitive methods, which requires us to understand the concepts and principles and have strong analytical ability.

Concise memory formula

Permutation and combination formula and binomial theorem formula;

The two principles of addition and multiplication are the laws that run through. What has nothing to do with order is combination, but what needs order is arrangement.

Two formulas, two properties, two ideas and methods. Arrange and combine the summary, and the application questions must be transformed.

It is common sense to arrange and combine together and choose the back row first. Special elements and positions should be considered first.

Don't worry too much, and don't miss too much. Punching is a skill. Arrange combinatorial identities and define proof modeling tests.

On binomial theorem, China Yang Hui Triangle. Two properties, two formulas, function assignment transformation.