English

If 20 points are marked on a circle, how many chords can be drawn? - Mathematics and Statistics

Advertisements
Advertisements

Question

If 20 points are marked on a circle, how many chords can be drawn?

Sum
Advertisements

Solution

There are 20 points on a circle.

To draw a chord, 2 points are required.

∴ the number of chords that can be drawn through 20 points on the circle

= 20C2

= `(20!)/(2!18!)`

= `(20 xx 19 xx 18!)/(2 xx 1 xx 18!)`

= 190.

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

RELATED QUESTIONS

Find the value of `""^20"C"_16 - ""^19"C"_16`


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


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 the number of triangles formed by joining 12 points if four points are collinear.


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


Find the differences between the largest values in the following: `""^14"C"_r  "and"  ""^12"C"_r`


Find the differences between the largest values in the following: `""^13"C"_r  "and"  ""^8"C"_r`


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


A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in the majority?


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 n and r if nPr = 720 and nCn–r = 120


If nPr = 1814400 and nCr = 45, find n+4Cr+3 


If nCr–1 = 6435, nCr = 5005, nCr+1 = 3003, find rC5


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


Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8


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 nC8 = nC12 


Find n if 2nCr–1 = 2nCr+1 


Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr


Find the differences between the greatest values in the following:

14Cr and 12Cr 


Find the differences between the greatest values in the following:

15Cr and 11Cr 


A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?


Select the correct answer from the given alternatives.

The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently


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.


A student passes an examination if he secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.


Answer the following:

Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.


Answer the following:

There are 4 doctors and 8 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team


If 'n' is positive integer and three consecutive coefficient in the expansion of (1 + x)n are in the ratio 6 : 33 : 110, then n 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×