English

Find the number of triangles formed by joining 12 points if no three points are collinear - Mathematics and Statistics

Advertisements
Advertisements

Question

Find the number of triangles formed by joining 12 points if no three points are collinear

Sum
Advertisements

Solution

A triangle can be formed by selecting 3 non-collinear points.

We can choose 3 points from 12 points in

12C3 = `(12!)/(3!9!)`

= `(12 xx 11 xx 10 xx 9!)/(3 xx 2 xx 1 xx 9!)`

= 220 ways

∴ number of triangles = 220.

shaalaa.com
Properties of Combinations
  Is there an error in this question or solution?
Chapter 3: Permutations and Combination - Exercise 3.6 [Page 65]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.6 | Q 14. (a) | Page 65

RELATED QUESTIONS

 Find the value of `""^15"C"_4  + ""^15"C"_5`


Find n if `""^"n""C"_("n" - 3)` = 84


Find r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10


If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.


If `""^"n""C"_("r" - 1)` = 6435, `""^"n""C"_"r"` = 5005, `""^"n""C"_("r" + 1)` = 3003, find `""^"r""C"_5`.


After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.


Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10


Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15


Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.


Find n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`


Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`


Find x if `""^"n""P"_"r" = "x"  ""^"n""C"_"r"`


Find r if `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`


find the value of `sum_("r" = 1)^4  ""^(21 - "r")"C"_4 + ""^17"C"_5`


Find the differences between the largest values in the following: `""^15"C"_r  "and"  ""^11"C"_r`


In how many ways can a boy invite his 5 friends to a party so that at least three join the party?


A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?


Five students are selected from 11. How many ways can these students be selected if two specified students are selected?


Find n if nCn–3 = 84


Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 8 green balls, and 7 blue balls so that 3 balls of every colour are drawn


After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.


There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection


A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 2 vowels are chosen?


Find n if 21C6n = `""^21"C"_(("n"^2 + 5))` 


Find n if 2nCr–1 = 2nCr+1 


Find the differences between the greatest values in the following:

15Cr and 11Cr 


Answer the following:

Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections


Answer the following:

A student finds 7 books of his interest but can borrow only three books. He wants to borrow the 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.


Answer the following:

30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so.


Answer the following:

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


If `1/(8!) + 1/(7!) = x/(9!)`, than x is equal to ______.


Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×