Question

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.

Solution

Correct option is

× 18!.

Let B1 and B2 be two brothers among 20 persons and let M be a person that will sit between B1 and B2. The person can be chosen from 18 persons (excluding B1 and B2) in 18 ways. Considering the two brothersB1 and B2 and person M as one person, we have 18 persons in all. These 18 persons can be arranged around a circle in (18 – 1)! = 17! Ways.

But B1 and B2 can be arranged among themselves in 2! = ways

Hence the total number of ways = 18 × 17! × 2!. = 2 × 18!.

SIMILAR QUESTIONS

Q1

There are three papers of 100 marks each in an examination. Then the no. of ways can a student get 150 marks such that he gets atleast 60% in two papers

Q2

If m parallel lines in plane are intersected by a family of n parallel lines. Find the number of parallelograms formed.

Q3

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

Q4

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

Q5

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.

Q6

Let 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 Pand another set Q is chosen at random then find the number of ways to form sets such that 

Q7

Let 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 Pand another set Q is chosen at random. Find  number of ways to  chosenand Q such that ∪ Q contains exactly r elements.

Q8

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

Q9

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:

Q10

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?