Example 1.3.3 | Chapter 1 | Permutations and Combinations | Combinatorics

Example 1.3.3 | Chapter 1 | Permutations and Combinations | Combinatorics

Example No 1.3.3 | Permutations | Chapter 1 | Permutations and Combinations | Combinatorics

Example 1.3.3 | Permutations | Chapter 1 | Permutations and Combinations | Principles and techniques in Combinations

Book : Principles and Techniques in Combinatorics.

Chapter Number : 01
Chapter Name : Permutations and Combinations.

Lecture Number : 10

Topic : Permutations

Example: 1.3.3

Problems ( Exercise ) : 00
Question Number : 00

Part Number : 00
Question :
Example: 1.3.3
Find the number of ways to seat n married couples around a table in each of the following cases:
1) Man and Woman alternate ;
2) Every Woman in next to her husband.

Find the number of ways to seat n married couples around a table in each of the following cases:
1) Man and Woman alternate ;
Sol:

Total Couplers = n
Total Man = n
Total Woman = n
First we seated “ n ” man around the table.
Q(n,n) = (n – 1)!
Second The “ n ” Woman can then be seated in the “ n ” Spaces between two men.
P(n,n) = n!/(n – n)! = n!
Thus the number of such arrangements is
(n – 1)! . n!

Find the number of ways to seat n married couples around a table in each of the following cases:
2) Every Woman in next to her husband.
Sol:

“First” Each couple is first treated as an entity. The number of ways to arrange the “ “ n ” entities around the table.
Q(n,n) = (n – 1)!
“Second” the two people in each entity can be permuted in 2! Ways. The desired number of ways is

(n – 1)! . 2^n