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If 4 points are indicated on a line and 5 points are indicat
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08 May 2018, 04:00
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If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?
Re: If 4 points are indicated on a line and 5 points are indicat
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08 May 2018, 07:07
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amorphous wrote:
If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?
A) 20 B) 30 C) 40 D) 70 E) 90
There are two ways to create these triangles: 1) select 2 points from the first line (the line with 4 points) and select 1 point from the second line (the line with 5 points) 2) select 1 point from the first line (the line with 4 points) and select 2 points from the second line (the line with 5 points)
Once we have selected 3 points, we simply connect them with lines to form a triangle
We'll handle each option separately.
---------------------------------------- 1) select 2 points from the first line (the line with 4 points) and select 1 point from the second line (the line with 5 points) Take the task of selecting points and break it into stages.
Stage 1: Select two points from the first line Since the order in which we select the points does not matter, we can use combinations. We can select 2 points from 4 points in 4C2 ways (6 ways) So, we can complete stage 1 in 6 ways
Stage 2: Select one point from the second line There are 5 points to choose from, so we can complete this stage in 5 ways.
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create triangles) in (6)(5) ways (= 30 ways) ----------------------------------------
2) select 1 point from the first line (the line with 4 points) and select 2 points from the second line (the line with 5 points) Stage 1: Select one point from the first line There are 4 points to choose from, so we can complete this stage in 4 ways.
Stage 2: Select two point from the second line Since the order in which we select the points does not matter, we can use combinations. We can select 2 points from 5 points in 5C2 ways (10 ways) So, we can complete stage 2 in 10 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create triangles) in (4)(10) ways (= 40 ways) --------------------------------------------
TOTAL number of triangles = 30 + 40 = 70
Answer: D
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Re: If 4 points are indicated on a line and 5 points are indicat
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30 Apr 2021, 21:17
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