First of all, we need to understand the concept of permutation and combination to help us solve this problem. Arrangement refers to taking out a specified number of elements from a given number of elements for sorting.
Combination refers to taking out a specified number of elements from a given number of elements, regardless of sorting. This problem, we are actually considering the arrangement, because the four-digit password needs to consider the order.
The first digit has 10 choices (0-9), the second digit has 9 choices (because the first digit cannot be repeated), the third digit has 8 choices, and the fourth digit has 7 choices.
Therefore, the overall layout is 10×9×8×7. Using the mathematical formula, we can express it as: total number of permutations = 10! /( 10-4)! , in which'!' Represents factorial. Now let's calculate. The calculation result is that there are 5040 four-digit passwords.
Classification and characteristics of 0-9 digital four-digit passwords;
The characteristic of 0-9 four-digit password is that each bit has 10 possible choices, so it can form the fourth power of 10, that is, 10000 different passwords. Because repeated numbers are not allowed in passwords, these passwords can be divided into two categories:
The first category is that numbers can't be repeated and 0 can't be put in the first place. In this case, the first digit has 9 choices (from 1-9), the second digit has 8 choices (from 0-9, excluding the used digits of the first digit), the third digit has 7 choices (from 0-9, excluding the used digits of the first two digits), and the fourth digit has 6 choices (from 0-9, excluding the first two digits) Therefore, the total number of passwords in this case is 9×8×7×6=3024.
The second category is that numbers can be repeated and 0 can be put in the first place. In this case, each bit has 10 choices (from 0 to 9), so the total number of passwords is the fourth power of 10, that is, 10000.
Diversity of combinations: Because each bit has 10 choices, many different combinations can be formed. Even if the numbers cannot be repeated, many different passwords can be formed by different combinations.
Easy to remember: Because 0-9 is the most familiar number in people's daily life, this password is easy to remember. Especially some important passwords, such as bank accounts, e-mail, etc. , using this password can improve security.
Cracking difficulty: It is relatively difficult for a password cracker to crack the 0-9 four-digit password. Even if the computer is used for violent cracking, it will take a long time and computing resources.