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13 Feb 2013, 23:56
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
55% (02:00) correct
45%
(02:06)
wrong
based on 218
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Two highways start from a point P and meet again at the point Q. Between P and Q there are 5 subways, joining the highways at 5 different places. How many different routes are possible for a journey from P to Q?
(A) 12
(B) 16
(C) 24
(D) 32
(E) 64
not sure, how to work with this kind of problem
(A) 12
(B) 16
(C) 24
(D) 32
(E) 64
not sure, how to work with this kind of problem
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14 Feb 2013, 02:21
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mynhauzen
No. of ways of using no subways = \(2*5C_0 = 2*1 = 2\)
No. of ways of using one subway = \(2*5C_1 = 2*5 = 10\)
No. of ways of using two subways = \(2*5C_2 = 2*10 = 20\)
No. of ways of using three subways = \(2*5C_3 = 2*10 = 20\)
No. of ways of using four subways = \(2*5C_4 = 2*5 = 10\)
No. of ways of using five subways = \(2*5C_5 = 2*1 = 2\)
We are multiplying by 2 on each occasion because for each combination, we can start the trip either by route 1 or by route 2.
Total = 2 + 10 + 20 + 20 + 10 + 2 = 64
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14 Feb 2013, 02:23
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If one starts its journey from point P, one has 2 options ( to go via either highway)... When he reaches 1st subway point he has again, 2 options, to continue on the highway or to go through subway., When he reaches next subway, he will have same two options, of course we are considering that he doesn't return from any point.
Since, there are 5 subways, he has the option of choosing from 2 choices 6 times (one when he just starts his journey). So, total ways he can reach is destination is 2^6 = 64.
Since, there are 5 subways, he has the option of choosing from 2 choices 6 times (one when he just starts his journey). So, total ways he can reach is destination is 2^6 = 64.
