Brent@GMATPrepNow wrote: ↑Wed Feb 03, 2021 10:27 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
Brent Hanneson - Creator of GMATPrepNow.com
