There are n points in a plane of which p poin | vedclass

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

Question

(C) Total number of points is $n$. The number of ways to select $2$ points from $n$ points to form a line is $^nC_2$.Since $p$ points are collinear,th

Vedclass · Accepted Answer

$^nC_2 - ^pC_2 + 1$

Vedclass · Answer

(C) Total number of points is $n$. The number of ways to select $2$ points from $n$ points to form a line is $^nC_2$.Since $p$ points are collinear,they all lie on the same line. Selecting any $2$ points from these $p$ points results in the same line,which is counted $^pC_2$ times in $^nC_2$.To correct this,we subtract all the lines formed by the $p$ collinear points $(^pC_2)$ and add back $1$ to account for the single line that passes through all $p$ points.Therefore,the total number of distinct lines is $^nC_2 - ^pC_2 + 1$.

There are $n$ points in a plane of which $p$ points are collinear. How many lines can be formed from these points?

Similar Questions

If $(n+1)! = 6[(n-1)!]$,find $n$.

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ (for $n=1, 2, 3$) is:

If the letters of the word $SACHIN$ are arranged in all possible ways and these words are written out as in a dictionary,then the word $SACHIN$ appears at serial number:

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

Vedclass Test Series

Exam Paper Generator

Online Exam Module