gmat_guy666 wrote:How many straight lines can be formed using 10 points , 4 of which are collinear ?
A) 20
B) 30
C) 40
D) 50
E) 60
That's a very vague (ambiguous) question.
Do the lines need to pass through any of the points? Is passing through 1 point enough? 2 points? 3 points?
Given that the correct answer is
C, I assume the question should be worded as follows:
If a line is defined two points, how many different lines can be formed with 10 points, 4 of which are collinear ?
NOTE:
IF none of the points were collinear (all in a row), then the number of lines = 10C2 (10 points, choose 2 of them).
10C2 =
45, so if we IGNORE the fact that some points are collinear, the answer is
45.
HOWEVER, we need to subtract the lines that can be created using 2 of the 4 collinear points, since these lines will all be the SAME.
In how many ways can we select 2 points from the 4 collinear points?
We can do this in 4C2 ways (=
6 ways)
In other words, all
6 possible lines are the SAME line.
So, we have counted 5 extra lines.
45 - 5 = 40
Answer:
C
Aside: If anyone is interested, we have a free video on calculating combinations (like 10C2 and 4C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
Cheers,
Brent
