But i guess,first vertex is fixed after that we have only 6 ways and traversing them in both directions give 12.

0 votes

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

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.

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......

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**