Permutations And Combinations Question 67
Question: Six points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points of intersection is equal to
Options:
A) 105
B) 45
C) 51
D) None of these
Correct Answer: C
Show Answer
Answer:
Solution:
$ \therefore $ $ A_1 $ occurs $ ^{5}C_2=10 $ times in 105 points of intersections. Similar is the case with other five points.
$ \therefore $ 6 original points come $ 6\times 10=60 $ times in points of intersection. Hence the number of distinct points of intersection $ =105-60-6=40 $ .
BETA
