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08 Dec 2014, 06:24
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:21) correct
32%
(01:41)
wrong
based on 256
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
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
08 Dec 2014, 07:37
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Bookmarks
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
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
