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16 Nov 2017, 01:44
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Difficulty:
45%
(medium)
Question Stats:
62% (01:42) correct
38%
(01:49)
wrong
based on 298
sessions
History
Date
Time
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Not Attempted Yet
[GMAT math practice question]
In how many ways can three boys and four girls line up in a row, if girls take the first and last positions?
A. 28
B. 120
C. 720
D. 1,440
E. 5,040
In how many ways can three boys and four girls line up in a row, if girls take the first and last positions?
A. 28
B. 120
C. 720
D. 1,440
E. 5,040
17 Nov 2017, 14:37
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MathRevolution
[GMAT math practice question]
In how many ways can three boys and four girls line up in a row, if girls take the first and last positions?
A. 28
B. 120
C. 720
D. 1,440
E. 5,040
In how many ways can three boys and four girls line up in a row, if girls take the first and last positions?
A. 28
B. 120
C. 720
D. 1,440
E. 5,040
The number of ways we can choose 2 girls from 4 to take the first and last positions is 4C2 = (4 x 3)/2! = 12/2 = 6. Once the two girls, say, A and B, are picked, there are two ways to switch them, since A can be the first position and B the last or B can be the first position and A the last. The 5 people in the middle can be arranged in 5! = 120 ways. Thus, the total number of ways we can arrange these 7 people so that the first and last positions are taken by girls is:
6 x 2 x 120 = 1,440
Answer: D
General Discussion
16 Nov 2017, 03:07
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MathRevolution
[GMAT math practice question]
In how many ways can three boys and four girls line up in a row, if girls take the first and last positions?
A. 28
B. 120
C. 720
D. 1,440
E. 5,040
In how many ways can three boys and four girls line up in a row, if girls take the first and last positions?
A. 28
B. 120
C. 720
D. 1,440
E. 5,040
In the row, first and last place shall be taken by girls
No. of ways of filling first place and last place out of 4 girls = 4x3 = 12
No. of ways of filling remaining places = 5x4x3x2x1 = 120 (because 2 girls are already placed in 2 positions remaining 5 persons are remaining)
Total no. of ways = 12 x 120 =1440
Answer (D) 1440
