用数字重复的数字 1、2、3、4、5 可以组成多少个 4 位数字？
在数学中，排列涉及将一个组的所有成员排序为某个系列或排列的函数。换句话说，如果该组已经被定向，则其组件的重定向称为置换过程。排列几乎在每个数学领域都以或多或少重要的方式发生。当在某些有限的地方观察到不同的命令时，它们经常出现。
排列
排列被称为按顺序组织组、主体或数字的过程，从集合中选择一个或多个数字，被称为组合，使得整数的序列不受影响。
置换公式
在排列中，从一组 n 个项目中收集 r 个项目，没有任何替换。在这个收集物质的序列中。
nPr = (n!)/(n – r)!
Here,
n = set dimensions, the total number of object in the set
r = subset dimensions, the number of objects to be choose from the set
组合
组合是从组中选择对象的一种方式，这样（与排列不同）选择的顺序无关紧要。在较小的情况下，总而言之，可以想象组合的数量。组合是指一次取k个对象，不重复地组合n个对象。提到允许重复的组合，经常使用表达式 k-selection 或 k-combination with repeat。
组合配方
结合起来，从一组 n 个对象中选择 r 个对象，其中选择的顺序无关紧要。
nCr = n!⁄((n – r)! r!)
Here,
n = Number of objects in group
r = Number of objects selected from the group
用数字重复的数字 1、2、3、4、5 可以组成多少个 4 位数字？
解决方案：
Repetition of digit is allowed. So, for the ones place we have 5 option i.e., 1,2,3,4,5 similarly for tens place we have again 5 option i.e., 1,2,3,4,5 for the hundredth place we have 5 option i.e., 1,2,3,4,5 similarly, for the thousandth place we have 5 option i.e., 1,2,3,4,5.
Total no. of four digit number = 5 × 5 × 5 ×5
= 625
类似问题
问题1：用数字0、1、2、3、4、5可以组成多少个6位数字。如果允许重复数字？
回答：
Repetition of digit is allowed. So, for the first place we have 6 option i.e., 0,1,2,3,4,5 similarly for second place we have again 6 option i.e., 0,1,2,3,4,5 for the third place we have 6 option i.e., 0,1,2,3,4,5 for the fourth place we have 6 option i.e., 0,1,2,3,4,5 and for the fifth thousandth place we have 6 option i.e., 0,1,2,3,4,5 and for the sixth place we have 5 option i.e., 1,2,3,4,5 we can’t take 0 at last place because if 0 will be filled at last place it will not become 6 digit number it will be taken as 5 digit number.
Total no. of six digit number = 4 × 5 × 5 × 5 × 5 × 5
= 12500
问题2：如果不允许数字重复，使用整数（3,5,7,9,1,0）可以设置多少个4位偶数？
回答：
For even number unit integer must be 0, Now the endure integers are 5 i.e., 3,5,7,9,1 now for the thousand place we have 5 choices for the hundredth place we have 4 choices and for the tens place we have 3 choices
Total no. of 4 digits even number can be found = 5 × 4 × 3
= 60
问题 3：使用数字 1、2、3、4、5、6 和 7（允许重复）可以找到多少个 8 位数字，使得数字从左到右或从右到左读法相同？
解决方案：
A eight digit number which reads the same left to right and right to left, means the last four digits are same as the first four digits but in the contrasting direction. So it is a four digit number.
Repetition of digit is allowed. So, for the first number we have 7 option similarly for second number we have again 7 option for the third number we have 7 option and for the fourth number we have 7 option.
So the possible numbers = 7 × 7 × 7 × 7
= 2,401
问题4：由数字1、2、3、4、5、6和7组成的六位数字的个数，使数字不重复，最后一个数字是偶数是
解决方案：
Since, last digits are even.
Therefore, For 1st place can be permeate in 3 ways and last place can be permeate in 2 ways and remaining places can be permeate in
5P4 = 120 ways
Hence, the number of six digit number, so that the last digits are even, is 3 × 120 × 2 = 720.