M7MBA wrote: ↑Sun Mar 14, 2021 5:28 am
In a plane, there are two parallel lines. One line has \(5\) points and another line has \(4\) different points. How many different triangles can we form from these \(9\) points?
A. 62
B. 70
C. 73
D. 86
E. 122
Answer:
B
Source: e-GMAT
There are two ways in which we can create a triangle.
#1) Select 2 points from the 5-point line and select 1 point from the 4-point line.
#2) Select 2 points from the 4-point line and select 1 point from the 5-point line.
#1) Select 2 points from the 5-point line and select 1 point from the 4-point line.
Take this task and break it into stages.
Stage 1: Select 2 points from the 5-point line
Since the order of the 2 selected points does not matter, we can use combinations.
We can select 2 points from 5 points in 5C2 =
10 ways.
If anyone is interested, a video on calculating combinations (like 5C2) in your head can be found at the bottom of this post
Stage 2: Select 1 point from the 4-point line.
We can complete this stage in
4 ways
By the Fundamental Counting Principle (FCP) we can complete the 2 stages in
(10)(4) ways (=
40 ways)
#2) Select 2 points from the 4-point line and select 1 point from the 5-point line.
Take this task and break it into stages.
Stage 1: Select 2 points from the 4-point line
We can select 2 points from 4 points in 4C2 =
6 ways.
Stage 2: Select 1 point from the 5-point line.
We can complete this stage in
5 ways
By the Fundamental Counting Principle (FCP) we can complete the 2 stages in
(6)(5) ways (=
30 ways)
-------------------------------------------------------------
So, the
TOTAL number of triangles =
40 +
30
= 70
Answer: B
Cheers,
Brent
