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

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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:
$\frac{8!}{5! \times 3!} = 56$

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

The correct option is A 56Let 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

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:
$\frac{8!}{5! \times 3!} = 56$