由 2 男 3 女组成的 1 男 2 女委员会有多少种方式？
排列被称为按顺序组织组、主体或数字的过程，从集合中选择主体或数字，被称为组合，其中数字的顺序无关紧要。
在数学中，排列也被称为组织一个群的过程，其中一个群的所有成员都被排列成某种顺序或顺序。如果组已经排列，则置换过程称为对其组件的重新定位。排列发生在几乎所有数学领域。它们大多出现在考虑某些有限集合上的不同命令时。
置换公式
在排列中，从一组 n 个事物中挑选出 r 个事物，没有任何替换。在这个挑选的顺序。
nPr = (n!)/(n – r)!
Here,
n = group size, the total number of things in the group
r = subset size, the number of things to be selected from the group
组合
组合是从集合中选择数字的函数，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。这种组合被称为一次合并n个事物而不重复。组合起来，顺序无关紧要，您可以按任何顺序选择项目。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。
组合配方
组合 r 个东西是从一组 n 个东西中挑选出来的，挑选的顺序无关紧要。
nCr =n!⁄((n-r)! r!)
Here,
n = Number of items in set
r = Number of things picked from the group
Note: In the same example, we have dissimilar instance for permutation and combination. For permutation, AB and BA are two different object but for choosing, AB and BA are same.
由 2 男 3 女组成的 1 男 2 女委员会有多少种方式？
回答：
Here we use the formula for choosing r objects from n different objects.
Complete step-by-step answer:
The number of ways of choosing r objects from n different objects is given by nCr and
the value of nCr is given as nCr = n! ⁄ r!(n−r)!
Here sequence doesn’t matter
The formula of selecting 1 man from 2 men: 2C1
= 2! ⁄ 1!(2-1)!
= 2! ⁄ 1!1!
= 2
The formula of selecting 2 women from 3 women: 3C2
= 3! ⁄ 2!(3-2)!
= 3! ⁄ 2!1!
= 3×2! ⁄ 2!
= 3
No of ways of selecting 1 man and 2 women = 2C1 × 3C2
= 2×3
= 6
Total number of Person = 2 Men + 3 Women = 5
Person required in committee = 3
No of ways = 5C3 = 10
类似问题
问题1：4人一组由3男4女组成。有多少种方法可以做到这一点？这些委员会中有多少由 2 名男性和 2 名女性组成？
回答：
Here we use the formula for choosing r objects from n dissimilar objects.
Complete step-by-step answer:
The number of ways of choosing r objects from n different objects is given by nCr and
the value of nCr is given as n Cr = n! ⁄ r!(n−r)! .
Here sequence doesn’t matter
The formula of selecting 2 man from 3 men: 3C2
= 3! ⁄ 2!(3-2)!
= 3! ⁄ 2!1!
= 3×2!/2!
= 3
The formula of selecting 2 women from 4 women: 4C2
= 4! ⁄ 2!(4-2)!
= 4! ⁄ 2!2!
= 4×3×2! ⁄ 2!×2!
= 4×3/2
= 2×3
= 6
No of ways to make a committee of 3 person = 3C2 × 4C2
= 3×6
= 18ways
Total number of Person = 3 Men + 4 Women = 7
Person required in committee = 4
No of ways = 7C4 = 35
问题2：一组6人，由4男4女组成。有多少种方法可以做到这一点？这些委员会中有多少由 3 名男性和 3 名女性组成？
回答：
Here we use the formula for choosing r objects from n different objects.
Complete step-by-step answer:
The number of ways of choosing r objects from n different objects is given by nCr and
the value of nCr is given as nCr = n! ⁄ r!(n−r)! .
Here sequence doesn’t matter
The formula of selecting 3 man from 4 men: 4C3
= 4! ⁄ 3!(4-3)!
= 4! ⁄ 3!1!
= 4×3!/3!
= 4
The formula of selecting 3 women from 4 women: 4C3
= 4! ⁄ 3!(4-3)!
= 4! ⁄ 3!1!
= 4×3! ⁄ 3!
= 4
No of ways to make a committee of 6 person = 4C3 × 4C3
= 4×4
= 16 ways
Total number of Person = 4 Men + 4 Women = 8
Person required in committee = 6
No of ways = 8C6 = 28
问题3：由10名男性和8名女性组成一个12人的团队。有多少种方法可以做到这一点？这些委员会中有多少个由 7 名男性和 5 名女性组成？
回答：
Here we use the formula for choosing r objects from n different objects.
Complete step-by-step answer:
The number of ways of choosing r objects from n different objects is given by nCr and
the value of nCr is given as nCr = n! ⁄ r!(n−r)! .
Here sequence doesn’t matter
The formula of selecting 7 man from 10 men: 10C7
= 10! ⁄ 7!(10-7)!
= 10! ⁄ 7!3!
= 10×7!/3!
= 120
The formula of selecting 5 women from 8 women: 8C5
= 8! ⁄ 5!(8-5)!
= 8! ⁄ 5!3! = 8×7×6×5!/5!×3×2×1
= 4×7×2
= 56
No of ways to make a committee of 12 person = 10C7 × 8C5
= 120 × 56
= 6,720 ways
Total number of Person = 10 Men + 8 Women = 18
Person required in committee = 12
No of ways = 18C12 = 18,564
问题4：由7男5女组成一组9人。有多少种方法可以做到这一点？这些委员会中有多少由 6 名男性和 3 名女性组成？
回答：
Here we use the formula for choosing r objects from n different objects.
Complete step-by-step answer:
The number of ways of choosing r objects from n different objects is given by nCr and
the value of nCr is given as nCr= n! ⁄ r!(n−r)! .
Here sequence doesn’t matter
The formula of selecting 6 man from 7 men: 7C6
= 7! ⁄ 6!(7-6)!
= 7! ⁄ 6!1!
= 7×6!/6!
= 7
The formula of selecting 3 women from 5 women: 5C3
= 5! ⁄ 3!(5-3)!
= 5! ⁄ 3!2!
= 5×4×3! ⁄ 3!×2×1
= 10
No of ways to make a committee of 6 person = 7C6 × 5C3
= 7×10
= 70 ways
Total number of Person = 7 Men + 5 Women = 12
Person required in committee = 9
No of ways = 12C9 = 220