The streets in a city are arranged like the lines of a chess-board. There are six streets running north and south, and five streets running along east-west. Find the number of ways in which a man can travel from the north-west to the south-east corner, going the shortest possible distance.

231

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462

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683

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900

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Solution

The correct option is A 462
1 2 3 4 5
2
3
4
If going by shortest route,
Total horizontal steps required $= 5$
Total vertical steps downward $= 6$
Total number of ways of arranging $5 H$ and $6 V$ steps = $^{11} P_{6} = 462$

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