用数字 1、2、3、4 和 5 可以组成多少个 3 位偶数？
在数学中，排列被称为排列一个集合的过程，其中一个集合的所有成员被排列成一些系列或顺序。如果集合已经排列，则排列的过程称为对其组件的重新排列。几乎所有数学领域都以或多或少的重要方式发生排列。当考虑某些有限集上的不同命令时，它们经常出现。
什么是组合？
组合是从组中选择项目的行为，这样（不像排列）选择的顺序无关紧要。在较小的情况下，可以计算组合的数量。组合是指一次取 k 的 n 个事物的并集，不重复。组合起来，您可以按任意顺序选择项目。对于那些允许重复出现的组合，经常使用术语 k-selection 或 k-combination with replication。
置换公式
在排列中，从 n 个事物的集合中选择 r 个事物，没有任何替换。在这个选择的顺序。
nPr = (n!) / (n-r)!
Here,
n = set size, the total number of items in the set
r = subset size , the number of items to be selected from the set
组合配方
组合 r 个事物是从一组 n 个事物中选择的，其中选择的顺序无关紧要。
nCr = n!/(n−r)!r!
Here,
n = Number of items in set
r = Number of items selected from the set
用数字 1、2、3、4 和 5 可以组成多少个 3 位偶数？
解决方案：
If repetition is allowed
A three digit even number is to be formed from given 5 digits 1,2,3,4,5.
Ones place can be filled by 2 or 4 since the number is to be even. So, there are 2 ways to fill ones place.
Since, repetition is allowed , so tens place can be filled by 5 ways.
Likewise, hundreds place can also be filled by 5 ways.
So, number of ways in which three digit even numbers can be formed is 5 × 5 × 2 = 50
If repetition is not allowed
A three digit even number is to be formed from given 5 digits 1,2,3,4,5.
Ones place can be filled by 2 or 4 since the number is to be even. So, there are 2 ways to fill ones place.
Since, repetition is not allowed, so tens place can be filled by 4 ways.
Similarly, hundreds place can be filled by 3 ways.
So, number of ways in which three digit even numbers can be formed is 2 × 4 × 3 = 24
类似问题
问题1：用数字1、2、3、4和5可以组成多少个3位奇数？
解决方案：
If repetition is allowed
A three digit odd number is to be formed from given 5 digits 1,2,3,4,5.
Ones place can be filled by 1, 3 or 5 since the number is to be odd. So,
there are 3 ways to fill ones place.
Since, repetition is allowed , so tens place can be filled by 5 ways.
Similarly, hundreds place can also be filled by 5 ways.
So, number of ways in which three digit odd numbers can be formed is 5×5×3=75
If repetition is not allowed
A three digit odd number is to be formed from given 5 digits 1,2,3,4,5.
Since, for the number is to be odd , so ones place can be filled by 1, 3 or 5. So,
there are 3 ways to fill ones place.
Since, repetition is not allowed , so tens place can be filled by 4 ways.
Similarly, hundreds place can be filled by 3 ways.
So, number of ways in which three digit odd numbers can be formed is 3×4×3 =36
问题2：用数字1、2、3、4和5可以组成多少个4位偶数？
解决方案：
If repetition is allowed
A four digit even number is to be formed from given 5 digits 1,2,3,4,5.
Since, for the number is to be even, so ones place can be filled by 2 or 4. So, there
are 2 ways to fill ones place.
Since, repetition is allowed, so tens place can be filled by 5 ways.
Similarly, hundreds place can also be filled by 5 ways.
Similarly, thousandth place can also be filled by 5 ways
So, number of ways in which four digit even numbers can be formed is 5 × 5 × 5 × 2 = 250
If repetition is not allowed
A four digit even number is to be formed from given 5 digits 1,2,3,4,5.
Since, for the number is to be even, so ones place can be filled by 2 or 4. So,
there are 2 ways to fill ones place.
Since, repetition is not allowed, so tens place can be filled by 4 ways.
Similarly, hundreds place can be filled by 3 ways.
Similarly, thousandth place can be filled by 2 ways
So, number of ways in which four digit even numbers can be formed is 2 × 4 × 3 × 2 = 48