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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?
Options
72
144
14
19
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Solution
72
Explanation:
In the following figure:
There are 4 bus routes from A to B and 3 routes from B to C.
Therefore, there are 4 × 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 can not use same bus routes from C to B and B to A more than once.
Thus, there are 2 × 3 = 6 routes for return journey.
Therefore, the required number of ways = 12 × 6 = 72.
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