Q. 105.0( 1 Vote )

# m men and n women are to be seated in a row so that no two women sit together. If m>n then show that the number of ways in which they can be seated as

Given: there are m men and n women where m>n

To find: out their possible way of sitting arrangements in a row such that no two women sit together

Let m = 2 then possible arrangement is

_ m _ m _

Here 3(2 + 1) gaps for women can by made by 2 men so that no two of them comes together

When m men are there, m seats can be occupied by men and m + 1 seat can by women

Formula used:

Number of arrangements of n things taken all at a time = P(n, n)

Total number of arrangements of men

= the number of arrangements of m things taken all at a time

= P(m, m)

{ 0! = 1}

= m!

Formula used:

Number of arrangements of n things taken r at a time = P(n, r)

Total number of arrangements of women

= the number of arrangements of m + 1 things taken n at a time

= P(m + 1, n)

Hence, total possible arrangements of m men and n women in a row such that no two women come together

Hence, Proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circular permutations61 mins
Challenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningFREE Class
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Understand Permutations like never before60 mins
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Interactive Quiz on Combinations-0253 mins
Interactive Quiz on Combinations50 mins
Division and distribution of objects58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses