A (1, 2) and B(5, 5) are two points. Starting from A, line segments of unit length are drawn either rightwards or upwards only, in each step, until B is reached. Then, the number of ways of connecting A and B in this manner is

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Solution

The correct option is A
35

Given A(1,2) and B(5,5). Difference of x-coordinates = 5 – 1 = 4 $∴$ Exactly 4 rightward steps are needed.
Difference of y-coordinates = 5 – 2 = 3.
$∴$ Exactly 3 upward steps are needed.
Note: Order of the steps is immaterial.
Denote each rightward step by R and each upward step by U. $∴$ The problem is arranging the letters RRRRUUU No. of arrangements = $\frac{7!}{4! 3!} = 35$

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