Home
Class 12
MATHS
m men and n women ae to be seated in a r...

`m` men and `n` women ae to be seated in a row so that no two women sit together. If `m > n` then show that the number of ways n which they fan be seated as `(m !(m+1)!)/((m-n+1)!)` .

Text Solution

Verified by Experts

The correct Answer is:
`((m+1)!m!)/((m-n+1)!)`
m men can be seated in m! ways, creating (m+1) places for n ladies to sit.
n ladies in (m+1) places can be arrnanged in `.^(m+1)P_(n)` ways.
`therefore` Total ways `=m!xx .^(m+1)P_(n)`
`m!xx((m+1)!)/((m+1-n)!)=((m+1)!m!)/((m-n+1)!)`
Promotional Banner

Similar Questions

Explore conceptually related problems

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 (m!(m+1)!)/((m-n+1)!) .

m men and n women are to be seated in a row that no two women sit together . If m gt n, then show that the mumber of ways in which they can be sated is (m!(m+1)!)/((m-n+1)!)

Find the number of ways in which 5 boys and 5 girls be seated in a row so that no two girls sit together

For 2 positive numbers m and n, which is the correct relation for (m+n) (1/m + 1/n)?

Find the number of ways in which 5 boys and 5 girls be seated in a row so that all the girls sit together and all the boys sit together

Find the number of ways in which 6 boys and 6 girls can be seated in a row so that all the girls sit together and all the boys sit together.

In which of the following, m gt n (m,n in R) ?

There are n seats round a table marked 1,2,3,…..n the number of ways in which m(len) persons can take seats is

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

Five boys and three girls are sitting in a row of 8 seats. Number of ways in which they can be seated so that not all the girls sit side by side is