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Let $A (1, 2), B (4, 6), C (9, 10)$ are 3 points in xy – plane starting from A line segments of unit length are drawn either right wards (or) upwards only in each step until C is reached. Then the no.of ways of connecting A and C through B is a four digited number then its units place digit is

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Detailed Solution

$A = (1, 2); B = (4, 6); C = (9, 10)$

From A to B there are 3 horizontal, 4 vertical, steps
From B to C there are 5 horizontal, 4 vertical steps

$∴$ No of shortest paths from A to C through

$B = (^{7} C_{3} \times^{9} C_{5}) = 35 \times 126 = 4410$

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