SOLUTION: 100 points are chosen at random in the plane. For how many integers n with 0 ≤ n ≤ 50 is it possible to draw a line with n points on one side of the line and 100 − n points o

Question 1163112: 100 points are chosen at random in the plane. For how many integers n with 0 ≤ n ≤ 50 is it possible to draw a line with n points on one side of the line and 100 − n points on the other side of the line?
(A) 50 (B) 25 (C) 26 (D) 51 (E) 49
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

It will certainly be possible to draw the line so that 0 of the points are on one side and all 100 will be on the other.

And, if the points are truly random, there is sure to be some way to draw the line so that 50 are on one side and 50 are on the other.

And there is no reason that you wouldn't be able to draw the line so that the distribution of the points on the two sides of the line were any other combination.

So n can be any integer from 0 to 50 inclusive; that is 51 different values.

ANSWER: (D) 51

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