Q4 of 64 Page 122

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

[Hint: Number of straight lines =18C2 – 5C2 + 1]

Formula:- (i)nCr


Given:-


Number of points =18


Number of Collinear points =5


Number of lines form by 18 points =18C2


For 5 points are collinear=5C2


the number of lines that can be formed joining the point.


=18C2-5C2+1



=153-10+1


=144


More from this chapter

All 64 →
2

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?

[Hint: In each case number of words beginning with A, C, H, I is 5!]

 3

A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

 5

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?

 6

How many committee of five persons with a chairperson can be selected from 12 persons. [Hint: Chairman can be selected in 12 ways and remaining in 11 C4.]