Question

There are $6$ roads between $A$ & $B$ and $4$ roads between $B$ & $C$.
i) In how many ways can one drive the circular trip (ii) without using the same road more than once.

Answer 1

i) There are $6\times 4=24$ ways to reach at C fom A and same ways to reach at A from C. Thus total ways are $24\times 24=576.$

ii) And in case of without using same road

When we came back we have $4-1=3$ ways from C to B and $6-1=5$ ways from B to A.

Thus total ways $=24\times (3\times 5)=360$