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Question

There are 6 roads between A and B and 4 roads between B and C.
(i) In how many ways can one drive from A to C by way of B?
(ii) In how many ways can one drive from A to C and back to A, passing through B on both trips?

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Solution

6 roads between A and B
4 roads between B and C
(i) A to C via B
A to B 6 ways, B to C 4 ways
A to C via B=6×4=24
(ii) A to C via B
C to A via B
A _ B _ C _ B _ A
6 4 4 6
No. of ways=6×4×4×6=24×24=576.

1180080_1194691_ans_db8e4ec7b28549ac8c439e03ff41748a.jpg

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