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

Since, m men and n women are to be seated in a row so that no two women sit together. This could be shown as
`xx M_(1) xx M_(2) xx M_(3) xx .. Xx M_(m) xx`
which shows there are (m + 1) places for n women.
`therefore` Numebr of ways in which they can be arranged
`= (m)! " "^(m + 1)P_(n)`
`= ((m)! * (m + 1)!)/((m + 1 - n)!)`
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 so that no two women sit next to each other. If mgen then the number of ways in which this can be done is

If sum of m terms is n and sum of n terms is m, then show that the sum of (m + n) terms is -(m + n).

The number of ways in which 5 ladies and 7 gentlemen can be seated in a round table so that no two ladies sit together, 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)):sqrt((m-m^2-n^2))dot

If n different objects are to placed in m places then the number of ways of placing is:

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

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

A coin is tossed (m+n) times with m>n. Show that the probability of getting m consecutive heads is (n+2)/2^(m+1)

2m white counters and 2n red counters are arranged in a straight line with (m+n) counters on each side of central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark is (A) .^(m+n)C_m (B) .^(2m+2n)C_(2m) (C) 1/2 ((m+n)!)/(m! n!) (D) None of these