从一副标准的 52 张牌中，有多少张 5 张牌完全由红牌组成？
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个不重复的n个事物的并集。组合可以以任意顺序选择项目。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
从一副标准的 52 张牌中，有多少张 5 张牌完全由红牌组成？
解决方案：
There are total 26 red card i.e., 13 hearts and 13 diamonds.
From 26 red cards, choose 5.
The answer is the binomial coefficient
(26C5) and you can read this as 26 choose 5.
So there are
(26C5) = 26! ⁄ 5!(26−5)!
= 26! ⁄ 5!21!
= 26×25×24×23×22×21! ⁄ 5×4×3×2×1×21!
= 26×25×24×23×22 ⁄ 5×4×3×2
= 26⁄2×25⁄5×24⁄12×23×22
= 13×5×2×23×22
= 13×10×23×22
= 130×506 = 65,780
Possible 5-card hands consisting of only red cards.
类似问题
问题 1：从标准的 52 张牌组中，有多少 6 张牌完全由黑牌组成？
解决方案：
There are total 26 black cards i.e., 13 clubs and 13 spades.
From 26 black cards, choose 6.
The answer is the binomial coefficient
(26C6) and you can read this as 26 choose 6.
So there are
(26C6) = 26! ⁄ 6!(26−6)!
= 26! ⁄ 6!20!
= 26×25×24×23×22×21×20! ⁄ 6×5×4×3×2×1×20!
= 26×25×24×23×22×21 ⁄ 6×5×4×3×2
= 26⁄2×25⁄5×24⁄24×23×22×21⁄3
= 13×5×23×22×7=13×115×154
= 1495×154 = 230,230
Possible 6-card hands consisting of only black cards.
问题 2：在标准的 52 张牌组中，有多少 2 张牌完全由黑牌组成？
解决方案：
There are total 26 black cards i.e., 13 clubs and 13 spades.
From 26 black cards, choose 2.
The answer is the binomial coefficient
26C2 and you can read this as 26 choose 2.
So there are
26C2 = 26! ⁄ 2!(26−2)!
= 26! ⁄ 2!24!
= 26×25×24! ⁄ 2×1×24!
= 26×25 ⁄ 2
= 26⁄2×25
= 13×25=13×25
= 325
Possible 2-card hands consisting of only black cards.