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, in how many ways can he make round trip?

• A. $14$
• B. $144$
• C. $72$
• D. $19$

Answer 1

The correct option is C $72$

Given, there are $4$ bus routes from $A$ to $B$ and $3$ routes from $B$ to $C$.
Therefore, there are $4\times 3=12$ ways to go from $A$ to $C$.
It is round trip so the man will 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.
There are $2\times 3=6$ routes for return journey.
[By using the fundamental principle of multiplication]
$\therefore$ The required number of ways $=12\times 6=72$
Hence, option (A) is correct.