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

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Math Expert
Joined: 02 Sep 2009
Posts: 47039
How many ways could three people sit at a table with five seats in whi [#permalink]

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08 Dec 2014, 06:24
00:00

Difficulty:

25% (medium)

Question Stats:

74% (00:49) correct 26% (01:32) wrong based on 152 sessions

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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

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Posts: 218
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
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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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08 Dec 2014, 06:36
1
2
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
Manager
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Posts: 155
Location: India
GMAT Date: 05-23-2015
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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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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

Math Expert
Joined: 02 Sep 2009
Posts: 47039
Re: How many ways could three people sit at a table with five seats in whi [#permalink]

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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

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Manager
Joined: 25 Dec 2012
Posts: 125
Re: How many ways could three people sit at a table with five seats in whi [#permalink]

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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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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.

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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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