The number of straight lines that can be form | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) To form a straight line,we need $2$ points. If no three points were collinear,the total number of lines would be $^{20}C_2$. However,$4$ points ar

Vedclass · Accepted Answer

$185$

Vedclass · Answer

(D) To form a straight line,we need $2$ points. If no three points were collinear,the total number of lines would be $^{20}C_2$. However,$4$ points are collinear,which means they form only $1$ line instead of $^{4}C_2$ lines. Therefore,the number of lines is given by the formula: $^{20}C_2 - ^{4}C_2 + 1$. Calculating the values: $^{20}C_2 = \frac{20 	imes 19}{2} = 190$. $^{4}C_2 = \frac{4 	imes 3}{2} = 6$. Required number of lines $= 190 - 6 + 1 = 185$.

The number of straight lines that can be formed by joining $20$ points,no three of which are in the same straight line,except $4$ of them which are in the same line.

Similar Questions

The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is:

Four-digit numbers are formed using the digits $1, 2, 3, 4$ (repetition is allowed). The number of such four-digit numbers divisible by $11$ is

In how many ways can the letters of the word '$LEADER$' be arranged?

$A$ box contains two white balls,three black balls,and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

If $a, b$ and $c$ are the greatest values of $^{19}C_{p}, ^{20}C_{q}$ and $^{21}C_{r}$ respectively,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module