CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Number of ways in which $$200$$ people can be divided in $$100$$ couples is


A
(200)!2100(100)!
loader
B
1×3×5....199
loader
C
(1012)(1022)....(2002)
loader
D
(200)!(100)!
loader

Solution

The correct option is A $$\dfrac {(200)!}{2^{100}(100)!}$$
1) Firstly, number of ways in which 200 people can be arranged at 200 places is $${ { 200 }_{ P } }_{ 200 }$$
$$=\frac { 200! }{ \left( 200-200 \right) ! } $$
$$=\frac { 200! }{ 0! } =200!$$           (1)

2) Now, these 200 people have been divided into 100 couples and order of couples is immaterial.
Thus, number of ways in which these 100 couples can be arranged at 100 places is $${ { 100 }_{ P } }_{ 100 }$$
$$=100!$$                   (2)
We have to divide (1) by (2)

3) Again, each pair of couple can be arranged in two different ways as order in which couple is formed is immaterial.
Thus, number of ways in which 100 couples can be arranged within themselves is, $$2\times 2\times 2\times ---------100\quad times$$
$$={ 2 }^{ 100 }$$            (3)

We have to divide (1) by (3)

Thus, total number of ways in which 200 people can be arranged in 100 couples is $$\frac { 200! }{ { 2 }^{ 100 }\times 100! } $$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image