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08 Jun 2020, 09:46
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (02:09) correct
61%
(02:36)
wrong
based on 96
sessions
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A railway passes through four towns A, B, C, and D. The railway forms a complete loop, as shown below, and trains go in both directions. Suppose that a trip between two adjacent towns costs one ticket. Using exactly eight tickets, how many distinct ways are there of traveling from town A and ending at town A? (Note that passing through 'A' somewhere in the middle of the trip is allowed.) 
Untitled.png [ 2.14 KiB | Viewed 2734 times ]
A. 48
B. 64
C. 96
D. 128
E. 150
Attachment:
Untitled.png [ 2.14 KiB | Viewed 2734 times ]
A. 48
B. 64
C. 96
D. 128
E. 150
10 Jun 2020, 07:29
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From Point A one can move either to B or C
Let's say moving Forward (i.e A to B) : F
moving Backward (i.e A to C) : B
Keeping this in Mind, we have these possible arrangements:
FFFFFFFFF: 1 (example - ABCDABCDA)
BBBBBBBB: 1 (example - ADCBADCBA)
FFFFBBBB: 8!/(4!4!) = 70 (example - ABCDADCBA / ABABABCBA)
FFFFFFBB: 8!/(6!2!) = 28 (example - ABCDABCBA)
BBBBBBFF: 8!/(6!2!) = 28 (example - ADCBADCDA)
Total: 1+1+70+28+28 = 128 ways
Let's say moving Forward (i.e A to B) : F
moving Backward (i.e A to C) : B
Keeping this in Mind, we have these possible arrangements:
FFFFFFFFF: 1 (example - ABCDABCDA)
BBBBBBBB: 1 (example - ADCBADCBA)
FFFFBBBB: 8!/(4!4!) = 70 (example - ABCDADCBA / ABABABCBA)
FFFFFFBB: 8!/(6!2!) = 28 (example - ABCDABCBA)
BBBBBBFF: 8!/(6!2!) = 28 (example - ADCBADCDA)
Total: 1+1+70+28+28 = 128 ways
General Discussion
08 Jun 2020, 10:04
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nick1816
Given: A railway passes through four towns A, B, C, and D. The railway forms a complete loop, as shown below, and trains go in both directions. Suppose that a trip between two adjacent towns costs one ticket.
Asked: Using exactly eight tickets, how many distinct ways are there of traveling from town A and ending at town A?
Possible trips = A(D/B)(A/C)(D/B)(A/C)(D/B)(A/C)(D/B)A
A trip ADADABABA represents how 8 tickets are spent travelling.
The number of distinct ways of traveling from town A and ending at town A \(= 2^7 = 128\)
IMO D
