मराठी

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
Advertisements

प्रश्न

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

उत्तर

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.2 [पृष्ठ १६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.2 | Q 14 | पृष्ठ १६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If nC8 = nC2, find nC2.


Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.


If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?


It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?


Compute:

 L.C.M. (6!, 7!, 8!)


A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?


From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?


Evaluate the following:

14C3


If 18Cx = 18Cx + 2, find x.


From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?


How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?


From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?


A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?


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 (i) diagonals


Find the number of (ii) triangles


A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?


If 20Cr = 20Cr−10, then 18Cr is equal to


If 20Cr + 1 = 20Cr − 1 , then r is equal to


There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?


If 43Cr − 6 = 43C3r + 1 , then the value of r is


If n + 1C3 = 2 · nC2 , then n =


The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is


A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.


Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.


The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______ 


A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?


All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.


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.


In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.


The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.


15C8 + 15C915C615C7 = ______.


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 ______.


Number of selections of at least one letter from the letters of MATHEMATICS, is ______.


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 no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.


From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×