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I tried solving it by enumerating all the paths and got ans 12.Can anyone provide some formula for this ?

in Quantitative Aptitude
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3 Answers

1 vote
Each node is connected to every other node. And solution is choosing nodes at each stage. First we have four options then after choosing it we have 3 options and then two options and finally we need to return to origin so only one choice. Answer is 4! = 24 ways.
–1
But i guess,first vertex is fixed after that we have only 6 ways and traversing them in both directions give 12.
–1
If start is fixed then answer is 6 only. How are you traversing in both directions? we need to go to each road only once.
0 votes
I think, there will  be factorial(4) =24 ways, Since in the question they did not give any information about Source. So any city can be Source and any city can be Destination.

Now Question has been reduced to 4 cities"

A BCD A

A BDC A

A CBD A

A CDB A

A DCB A

A DBC A

Similarly for all cities B,C and D

Answer will be 24 ways.

plz make me correct if i m wrong......
0 votes

Here we have 2 cases :

1. when we traverse 2 node in between source and destination . In that case we first have 3 choices and after that we have 2 options remaining..(3*2=6)

2. when we traverse all 3 node then in that case also we have first 3 choices then 2 and then 1...(3*2*1=6)

total way if we fixed first vertex is 6+6=12

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