Permutations And Combinations Question 76
Question: There are n points in a plane of which p points are collinear. How many lines can be formed from these points [Karnataka CET 2002]
Options:
A) $ ^{(n-p)}C_2 $
B) $ ^{n}C_2-{{}^{p}}C_2 $
C) $ ^{n}C_2-{{}^{p}}C_2+1 $
D) $ ^{n}C_2-{{}^{p}}C_2-1 $
Correct Answer: C Given, total number of points = n and number of collinear points = p. We know that one line has two end points. Therefore total number of lines = $ ^{n}C_2 $ . Since p points are collinear, therefore total number of lines drawn from collinear points = $ ^{p}C
C_2 $ . We also know that, corresponding to the line of collinearity, one will also be added. Therefore number of lines = $ ^{n}C_2-^{p}C_2+1. $
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Answer:
Solution:
BETA
