## Question

There are 5 gentlemen and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?

### Solution

2880

Five gentlemen can be seated at a round table in (5 – 1)! = 4! ways. Now, 5 places are created in which 4 ladies are to be seated. Select 4 seats for 4 ladies from 5 seats in ^{5}C_{4 }ways. Now 4 ladies can be arranged on the 4 selected seats in ways.

Hence, the total number of ways in which no two ladies sit together

#### SIMILAR QUESTIONS

There are *n* concurrent lines and another line parallel to one of them. The number of different triangles that will be formed by the (n + 1) lines, is

Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them, is

The sides *AB, BC* and *CA* of a triangle *ABC* have *a, b* and *c* interior points on them respectively, then find the number of triangles that can be constructed using these interior points as vertices.

Let *X *is a set containing n elements. A subset *P* of set *X* is chosen at random. The set *X* is then reconstructed by replacing the elements of set *P*and another set *Q* is chosen at random then find the number of ways to form sets such that

Let *X *is a set containing n elements. A subset *P* of set *X* is chosen at random. The set *X* is then reconstructed by replacing the elements of set *P*and another set *Q* is chosen at random. Find number of ways to chosen*P *and *Q* such that P ∪ Q contains exactly *r* elements.

In how many ways can 12 books be equally distributed among 3 students?

10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys so that exactly 2 children do not get any toy, is equal to:

There are 20 persons among whom are two brothers. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers.

In how many ways can a party of 4 men and 4 women be seated at a circular table so that no two women are adjacent?

Find the number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated.