English

There Are 10 Points in a Plane of Which 4 Are Collinear. How Many Different Straight Lines Can Be Drawn by Joining These Points. - Mathematics

Advertisements
Advertisements

Question

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Advertisements

Solution

Number of straight lines formed joining the 10 points, taking 2 points at a time = 

\[{}^{10} C_2 = \frac{10}{2} \times \frac{9}{1} = 45\]
Number of straight lines formed joining the 4 points, taking 2 points at a time =\[{}^4 C_2 = \frac{4}{2} \times \frac{3}{1} = 6\]
But, when 4 collinear points are joined pair wise, they give only one line.
∴ Required number of straight lines =\[45 - 6 + 1 = 40\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.2 [Page 16]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.2 | Q 14 | Page 16

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.


How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?


Compute:

\[\frac{11! - 10!}{9!}\]

How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?


How many different five-digit number licence plates can be made if

first digit cannot be zero and the repetition of digits is not allowed,


Since the  number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`


How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?


Evaluate the following:

14C3


24Cx = 24C2x + 3, find x.


If nC4 , nC5 and nC6 are in A.P., then find n.


In how many ways can a football team of 11 players be selected from 16 players? How many of these will

 exclude 2 particular players?


How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?


From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?


A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?


In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.


Find the number of diagonals of , 1.a hexagon


A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl?


In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?


A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?


In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?


How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?


If 20Cr = 20Cr + 4 , then rC3 is equal to


If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =


Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is


Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?


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?


A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.


A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red


If nC12 = nC8, then n is equal to ______.


A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.


There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C25C2.


If some or all of n objects are taken at a time, the number of combinations is 2n – 1.


Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.


A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.


A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.


There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.


The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×