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In a plane, there are two parallel lines. One line has 5 points and an

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Joined: 04 Jan 2015
Posts: 2456
In a plane, there are two parallel lines. One line has 5 points and an  [#permalink]

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Updated on: 13 Aug 2018, 05:28
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:38) correct 18% (02:15) wrong based on 108 sessions

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3 Deadly mistakes in Permutation and Combination - Exercise Question #1

1- 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?

Options
A. 62
B. 70
C. 73
D. 86
E. 122

Learn to use the Keyword Approach in Solving PnC question from the following article:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions

Article-3: 3 deadly mistakes you must avoid in Permutation & Combination

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Originally posted by EgmatQuantExpert on 18 Apr 2018, 04:23.
Last edited by EgmatQuantExpert on 13 Aug 2018, 05:28, edited 9 times in total.
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Re: In a plane, there are two parallel lines. One line has 5 points and an  [#permalink]

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Updated on: 23 Apr 2018, 03:44
1

Solution

Given:

•There are two parallel lines in a plane.
• One line has 5 points.
•Another line has 4 points.

To find:
• The number of different triangles using the 9 points on two lines.

Approach and Working out:

A triangle is formed by 3 different points.
Hence, we need to select 3 different points from 9 different points.
But, there is a catch.

• Can you form a triangle if all the three points lie on one line??
• No.

Let us call the line having 5 points as L1 and line having 4 different points as L2.

Since three different points give only one triangle, this is a combination question.

Thus, the possible cases to form a triangle are:
• Select two points on L1 and one point on L2
• Select two points on L2 and one point on L1.

Total ways to form the triangle= $$^5C_2$$* $$^4C_1$$ + $$^4C_2$$* $$^5C_1$$
• = 10*4+6*5= 40+30=70

Hence, option B is the correct answer.

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Originally posted by EgmatQuantExpert on 18 Apr 2018, 04:29.
Last edited by EgmatQuantExpert on 23 Apr 2018, 03:44, edited 2 times in total.
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Joined: 04 Apr 2018
Posts: 21
Re: In a plane, there are two parallel lines. One line has 5 points and an  [#permalink]

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18 Apr 2018, 22:59
1
9c3−4c3-5c3 = 70. Hence option B.
Manager
Joined: 30 Mar 2017
Posts: 134
GMAT 1: 200 Q1 V1
Re: In a plane, there are two parallel lines. One line has 5 points and an  [#permalink]

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19 Apr 2018, 15:00
1
There are 2 parallel lines. 5 points on one line, 4 points on the other line. To make a triangle, you need 2 points from one line and 1 point from the other line.

# of triangles = (# of ways to select 2 out of 5 points) and (# of ways to select 1 out of 4 points) or (# of ways to select 1 out of 5 points) and (# of ways to select 2 out of 4 points)

# of ways to select 2 out of 5 points: 5C2=10
# of ways to select 1 out of 4 points: 4C1=4
# of ways to select 1 out of 5 points: 5C1=5
# of ways to select 2 out of 4 points: 4C2=6

# of triangles = 10*4+5*6 = 70

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Re: In a plane, there are two parallel lines. One line has 5 points and an  [#permalink]

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23 Apr 2018, 03:57
Hey Everyone,

Official solution to the question has been posted.

Regards,
Ashutosh
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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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Manager
Joined: 31 Jan 2018
Posts: 69
Re: In a plane, there are two parallel lines. One line has 5 points and an  [#permalink]

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23 Apr 2018, 04:57
There are two parallel lines.

One line has five points and another has 4 points in it.

So while selecting points we can't select all the three points from the same line, since it will be colinear
Hence we will select two points from one line and other from second line, which gives us:
5C2*4C1 + 4C2*5C1 = 70
Re: In a plane, there are two parallel lines. One line has 5 points and an &nbs [#permalink] 23 Apr 2018, 04:57
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