Question

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

Answer 1

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