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Amy has to visit towns B and C in any order. The roads conne
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amorphous
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Amy has to visit towns B and C in any order. The roads conne [#permalink] New post  05 Feb 2018, 21:39
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Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A) 10
B) 8
C) 6
D) 4
E) 2
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pranab223
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Re: Amy has to visit towns B and C in any order. The roads conne [#permalink] New post  05 Feb 2018, 22:58
amorphous wrote:
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?




Can you share the source plz??
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pranab223
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Re: Amy has to visit towns B and C in any order. The roads conne [#permalink] New post  05 Feb 2018, 23:06
amorphous wrote:
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A) 10
B) 8
C) 6
D) 4
E) 2


Here we can assume few possibilities

1st : - let us go to B first, then C and back to A, then we have the following possibilities-
From A to B we have 1 way
From B to C we have 2 ways
From C to A we have 2 ways

Total number of ways = 1*2*2 = 4

2nd - let us go to C first then B and then back to A, we have the following possibilities-
From A to C we have 2 way
From C to B we have 2 ways
From B to A we have 1 way

Total number of ways = 2*2*1 = 4

Total number of ways = 4+4 = 8
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Re: Amy has to visit towns B and C in any order. The roads conne [#permalink] New post  06 Feb 2018, 20:48
pranab01 wrote:
amorphous wrote:
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?




Can you share the source plz??


I don't particularly remember the source though this is not from any test prep book or courses.
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