In the adjoining figure, the lines represent one-way roads

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

1. 15
2. 56
3. 120
4. 336

Correct Option: B

Here , number of vertical steps ( v ) = 3
Number of horizontal steps ( h ) = 5
Then in this case total number of ways is given by ^h+vC_h = ^h+vC_v = ⁸C₃ = 6 x 7 x ( 8/6 ) = 7 x 8 = 56.
Hence , 56 distinct routes can a car reach point B from point A .