Question:
Given a m*n matrix and a person is sitting in (0,0) box, and he has to go to the (m-1,n-1) box of the matrix .And the person can only go to right or down box from its current box position . We need to find out the number of ways he can reach from start to destination box .
Solution:
He needs to take total 'm-1 down' + 'n-1 right' steps
Given a m*n matrix and a person is sitting in (0,0) box, and he has to go to the (m-1,n-1) box of the matrix .And the person can only go to right or down box from its current box position . We need to find out the number of ways he can reach from start to destination box .
Solution:
He needs to take total 'm-1 down' + 'n-1 right' steps
Its classical Permutation and Combination problem.
Refer to theorem 3 on this page intmath.com/counting-probability/3-permutations.php
Refer to theorem 3 on this page intmath.com/counting-probability/3-permutations.php
Hence ans = (m+n-2)! / ((m-1)!*(n-1)!)
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