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Question

In the figure given below, the lines represent one way roads allowing travel only northwards or only eastwards. Along how many distinct routes can a car reach point A from point B?

A
56
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B
66
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C
76
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D
46
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Solution

The correct option is A 56
Let an eastward step be denoted by A and a northward step be denoted by B. There are 5 steps eastward and 3 steps northward. Therefore, we are trying to find the total number of ways of arranging AAAAABBB. This is equal to:
8!5!×3!=56

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