There are four bus routes between A and B; and three bus routes between B and C.


There are four bus routes between A and B; and three bus routes between B and C. A man can travel round trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, the number of ways he can make round trip, is

(a) 72

(b) 144

(c) 14

(d) 19


There are 4 bus routes from A to B and 3 bus routes from B to C.

Since, it is used trip so the man with travel back from $C$ to $A$ via $B$.

it is restricted that man cannot use same bus routes from C to B and B to A more than once.

So out of 4 options, 3 are Left from B to A and out of 3 options, 2 are Left from C to B.

∴ for return there are 3 × 2 options and from A to C there are 4 × 3 options.

∴ The required number of ways = 12 × 6 
= 72

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