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How many ways could three people sit at a table with five seats in whi

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How many ways could three people sit at a table with five seats in whi [#permalink]

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New post 08 Dec 2014, 06:24
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Tough and Tricky questions: Combinations.



How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?

A) 8
B) 12
C) 60
D) 118
E) 120

Kudos for a correct solution.

Source: Chili Hot GMAT
[Reveal] Spoiler: OA

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Re: How many ways could three people sit at a table with five seats in whi [#permalink]

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New post 08 Dec 2014, 06:36
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ways in which 3 seats out 5 can be selected = 5C3
ways in which 3 people can be arranged in 3 seats = 3!

Total ways of arrangement = 5C3*3!
=5*4/2*6
=10*6
=60

Ans = C
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Re: How many ways could three people sit at a table with five seats in whi [#permalink]

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New post 08 Dec 2014, 07:37
How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?

A) 8
B) 12
C) 60
D) 118
E) 120


Method 1
Number of ways 5 seats can be grouped as 3 seats= \(C^5_3\)=10
Number of arrangement within each group of 3 seats= 3!=6
Therefore total number of ways three people can seat in five seats = 10*3! =60

Method 2
Number of ways one person can seat in 5 seats = 5
Number of ways second person can seat after the first person has occupied a seat = 4
Number of ways third person can seat after first and second persons have occupied two seats = 3
Therefore, total number ways three people can seat in five seats = 5*4*3 = 60

Answer: C
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Re: How many ways could three people sit at a table with five seats in whi [#permalink]

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New post 09 Dec 2014, 06:49
Bunuel wrote:

Tough and Tricky questions: Combinations.



How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?

A) 8
B) 12
C) 60
D) 118
E) 120

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: How many ways could three people sit at a table with five seats in whi [#permalink]

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New post 28 Feb 2016, 20:46
Bunuel wrote:

Tough and Tricky questions: Combinations.



How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?

A) 8
B) 12
C) 60
D) 118
E) 120

Kudos for a correct solution.

Source: Chili Hot GMAT


5 Chairs 3 people need to be seated.

__ __ __ __ __

1st person can sit in 5 ways. Hence

5 __ __ __ __ __

2nd person can sit in only 4 ways since the 1st person occupied seat.

5 4 __ __ __

3rd person can sit in 3 ways since three empty chairs are there.

5 4 3 __ __

So total number of three person can sit in 5 chair is = 5*4*3 = 20*3 = 60
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Re: How many ways could three people sit at a table with five seats in whi [#permalink]

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New post 11 Apr 2018, 16:22
Quote:

How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?

A) 8
B) 12
C) 60
D) 118
E) 120


The number of choices for a seat the first person could have is 5. Once he has sat down, the number of choices for a seat the second person could have is 4. Finally, the number of choices for a seat the third person, after the first two have sat down, could have is 3. Thus, the number of ways 3 people can sit a table of with five seats is:

5 x 4 x 3 = 60

Alternate Solution:

The number of seats to be occupied can be selected in 5C3 = 5!/(3!*2!) = (5x4)/2 = 10 ways.

Once the seats to be occupied are determined, there are 3! = 6 ways the three people can be arranged in those seats.

In total, there are 10 x 6 = 60 ways the three people can sit at a table of five seats.

Answer: C
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Re: How many ways could three people sit at a table with five seats in whi   [#permalink] 11 Apr 2018, 16:22
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