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A man moves one unit distance for each step he takes. He always moves either parallel to the x-axis or y-axis. He starts at the point (0, 0) and reaches the point (1, 1) at the end of six steps. The number of ways he can do it is n. Find n. Please solve it.

A man moves one unit distance for each step he takes. He always moves either parallel to the x-axis or y-axis. He starts at the point (0, 0) and reaches the point (1, 1) at the end of six steps. The number of ways he can do it is n. Find n. Please solve it.

Grade:11

1 Answers

Arpit Pandey
35 Points
one year ago
the ways to reach 1,1 from 0,0 is three
so, we can,
go 3 up, 2 down and then one right which have 6!/(3!2!) moves.
and, 2 up, 1 down, 2 forward and 1 backward which have 6!/(3!3!) moves.
lastly, 1 up, 3 forward and one backward which have 6!/(3!2!) moves.
if we add the three possibilities, we get 140.
thus, total number of ways is 140*3 = 420.

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