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.
a + b + cC3 – (aC3 + bC3 + bC3)
Required number of triangles
= total number of ways of choosing 3 points – number of ways of choosing all the 3 points from AB or BC or CA
= a + b + cC3 – (aC3 + bC3 + bC3)
Find the sum of all four-digit numbers that can be formed using digits 0, 1, 2, 3, 4, no digits being repeated in any number.
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
If m parallel lines in plane are intersected by a family of n parallel lines. Find the number of parallelograms formed.
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
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.