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?
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 5C4 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
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 Pand 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 Pand another set Q is chosen at random. Find number of ways to chosenP 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.